Symplectic method for bending and vibration problems of one-dimensional hexagonal quasicrystal plates

Authors: Zhiqiang Sun, Tongtong An, Yanfen Qiao, Guolin Hou

Source: Applied Mathematical Modelling. 128:558-570

Subject Terms: free vibration, Free motions in linear vibration theory, deformation, Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics, Hamiltonian system, analytic solution, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces, quasicrystals, Variational principles and methods for infinite-dimensional Hamiltonian and Lagrangian systems

File Description: application/xml

Über eine Darstellung linearer Operatoren im Hilbertraum

Authors: Fenyö, Istvan

Source: Publicationes Mathematicae Debrecen. 25:123-137

Subject Terms: Genereralized Schmidt System, General (adjoints, conjugates, products, inverses, domains, ranges, etc.), Jordan-Normal Form, 0101 mathematics, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/3618821

ON MULTIPLE COMPLETENESS OF A SYSTEM OF EIGEN AND ADJOINT ELEMENTS OF OPERATOR SHEAF IN HILBERT SPACES: On multiple completeness of a system of eigen and adjoint elements of operator sheaf in Hilbert space

Authors: A.N. Dzhabrailova

Source: Chronos. 6:67-70

Subject Terms: Spectrum, resolvent, 0101 mathematics, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces, 01 natural sciences, Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)

File Description: application/xml

Access URL: https://zbmath.org/2189857

Two-fold completeness of root vectors of a system of quadratic pencils

Authors: Yakov Yakubov

Source: Journal de Mathématiques Pures et Appliquées. 84:1427-1454

Subject Terms: Completeness, Expansion, Mathematics(all), Applied Mathematics, eigenvectors, abstract pencils, 01 natural sciences, Abstract pencils, expansion, completeness, Abel basis, Eigenvalue problems for linear operators, Boundary-value problems with a parameter, boundary-value problems with a parameter, 0101 mathematics, Eigenvectors, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces

File Description: application/xml

Access URL: https://zbmath.org/2244565
https://doi.org/10.1016/j.matpur.2005.05.002
https://www.sciencedirect.com/science/article/abs/pii/S0021782405000577#!
https://core.ac.uk/display/82808596
https://www.sciencedirect.com/science/article/pii/S0021782405000577

A measure-theoretical approach to the nuclear and inductive spectral theorems

Authors: Manuel Gadella, Fernando Gómez

Source: Bulletin des Sciences Mathématiques. 129:567-590

Subject Terms: nuclear spectral theorem, Mathematics(all), martingale, Cyclic vectors, hypercyclic and chaotic operators, generalized eigenfunction expansion, General spectral theory of ordinary differential operators, 01 natural sciences, inductive spectral theorem, Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators, direct integral of Hilbert spaces, Nuclear spectral theorem, Rigged Hilbert space, Martingale, Generalized eigenfunction expansion, Inductive spectral theorem, rigged Hilbert space, 0103 physical sciences, Direct integral of Hilbert spaces, 0101 mathematics, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces, Vitaly system, Radon-Nikodym derivatives, spectral measures

File Description: application/xml

Access URL: https://zbmath.org/2229439
https://doi.org/10.1016/j.bulsci.2005.02.004
https://www.sciencedirect.com/science/article/abs/pii/S0007449705000254
https://www.sciencedirect.com/science/article/pii/S0007449705000254
https://core.ac.uk/display/82399816

Partial *-algebras of Distributions: Partial *-algebras of distributions

Authors: TRAPANI, Camillo, TSCHINKE, Francesco

Source: Publications of the Research Institute for Mathematical Sciences. 41:259-279

Subject Terms: Algebras of unbounded operators, partial algebras of operators, partial \(*\)-algebras, topological quasi-algebras, 0101 mathematics, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces, 16. Peace & justice, 01 natural sciences, Operations with distributions and generalized functions, multiplication of distributions

File Description: application/xml

Access URL: http://www.ems-ph.org/journals/show_pdf.php?issn=0034-5318&vol=41&iss=2&rank=1
https://zbmath.org/2230578
https://doi.org/10.2977/prims/1145475353
http://ci.nii.ac.jp/naid/110001239993
https://www.ems-ph.org/journals/show_pdf.php?issn=0034-5318&vol=41&iss=2&rank=1
https://www.ems-ph.org/doi/10.2977/prims/1145475353
https://www.kurims.kyoto-u.ac.jp/~prims/pdf/41-2/41-2-10.pdf
https://hdl.handle.net/10447/20465

Partial Multiplication of Operators in Rigged Hilbert Spaces: Partial multiplication of operators in rigged Hilbert spaces

Authors: TRAPANI, Camillo, TSCHINKE, Francesco

Source: Integral Equations and Operator Theory. 51:583-600

Subject Terms: Generalizations of inner products (semi-inner products, partial inner products, etc.), partial \(*\)-algebra, Algebras of unbounded operators, partial algebras of operators, interspaces in rigged Hilbert space, multiplication framework, 0101 mathematics, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces, quasi \(*\)-algebra, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007%2Fs00020-002-1263-z
https://link.springer.com/content/pdf/10.1007%2Fs00020-002-1263-z.pdf
https://core.ac.uk/display/53222534
https://hdl.handle.net/10447/4389

The expansion of a semigroup and a Riesz basis criterion

Authors: Xu, GQ, Yung, SP

Source: Journal of Differential Equations. 210:1-24

Subject Terms: 0209 industrial biotechnology, Boundary value problems for linear first-order PDEs, One-parameter semigroups and linear evolution equations, Heat Exchanger Equation, Heat exchanger equation, 02 engineering and technology, Riesz Basis, Semigroup expansion, 01 natural sciences, Riesz basis, heat exchanger equation, Semigroup Expansion, 0101 mathematics, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces, Analysis, semigroup expansion

File Description: application/xml

Access URL: https://zbmath.org/2136777
https://doi.org/10.1016/j.jde.2004.09.015
https://www.sciencedirect.com/science/article/pii/S0022039604004206
http://hub.hku.hk/handle/10722/156123
https://ui.adsabs.harvard.edu/abs/2005JDE...210....1X/abstract
http://www.sciencedirect.com/science/article/pii/S0022039604004206
https://core.ac.uk/display/37976731
http://hdl.handle.net/10722/156123

The role of the rigged Hilbert space in quantum mechanics

Authors: Rafael de la Madrid

Source: European Journal of Physics. 26:287-312

Subject Terms: Quantum Physics, Applications of functional analysis in quantum physics, Applications of operator theory in the physical sciences, quantum mechanics, FOS: Physical sciences, rigged Hilbert spaces, (Generalized) eigenfunction expansions of linear operators, Quantum Physics (quant-ph), continuous spectrum, Selfadjoint operator theory in quantum theory, including spectral analysis

File Description: application/xml

Access URL: http://arxiv.org/pdf/quant-ph/0502053
http://arxiv.org/abs/quant-ph/0502053
https://arxiv.org/pdf/quant-ph/0502053
https://core.ac.uk/display/22113302
https://arxiv.org/abs/quant-ph/0502053

Hilbert Spaces Unconditional Bases Consisting of Values of Entire Vector-Functions of Order 1/2: Hilbert spaces unconditional bases consisting of values of entire vector-functions of order 1/2

Authors: M. G. Volkova, G. M. Gubreev

Source: Journal of Mathematical Sciences. 124:4861-4866

Subject Terms: Integral operators, unconditional basis, Spaces of vector- and operator-valued functions, dissipative Volterra operator, finite exponential type, 0101 mathematics, Linear accretive operators, dissipative operators, etc, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces, separable Hilbert space, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/article/10.1023/B:JOTH.0000042447.85947.cd
https://link.springer.com/content/pdf/10.1023%2FB%3AJOTH.0000042447.85947.cd.pdf

The rigged Hilbert space of the algebra of the one-dimensional rectangular barrier potential

Authors: R. de la Madrid

Source: Journal of Physics A: Mathematical and General. 37:8129-8157

Subject Terms: Operator algebra methods applied to problems in quantum theory, High Energy Physics - Theory, Quantum Physics, Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.), General theory of ordinary differential operators, FOS: Physical sciences, Mathematical Physics (math-ph), 01 natural sciences, High Energy Physics - Theory (hep-th), 0103 physical sciences, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces, Quantum Physics (quant-ph), Mathematical Physics

File Description: application/xml

Access URL: http://arxiv.org/pdf/quant-ph/0407195
http://arxiv.org/abs/quant-ph/0407195
https://zbmath.org/2142958
https://doi.org/10.1088/0305-4470/37/33/011
https://core.ac.uk/display/157332782
https://ui.adsabs.harvard.edu/abs/2004JPhA...37.8129D/abstract
http://iopscience.iop.org/article/10.1088/0305-4470/37/33/011/meta
https://iopscience.iop.org/article/10.1088/0305-4470/37/33/011/pdf
http://iopscience.iop.org/article/10.1088/0305-4470/37/33/011/pdf
https://arxiv.org/abs/quant-ph/0407195
https://arxiv.org/pdf/quant-ph/0407195v1

Arrow of Time in Rigged Hilbert Space Quantum Mechanics: Arrow of time in rigged Hilbert space quantum mechanics

Authors: Robert C. Bishop

Source: International Journal of Theoretical Physics. 43:1675-1687

Subject Terms: Quantum Physics, \(2\)-body potential quantum scattering theory, quantum mechanics, FOS: Physical sciences, General and philosophical questions in quantum theory, arrow of time, Quantum measurement theory, state operations, state preparations, 06 humanities and the arts, 0603 philosophy, ethics and religion, 01 natural sciences, irreversibility, rigged Hilbert space, 0103 physical sciences, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces, Quantum Physics (quant-ph)

File Description: application/xml

Access URL: http://arxiv.org/pdf/quant-ph/0506184
http://arxiv.org/abs/quant-ph/0506184
https://zbmath.org/2146176
https://doi.org/10.1023/b:ijtp.0000048813.60909.8c
https://link.springer.com/article/10.1023%2FB%3AIJTP.0000048813.60909.8c
https://www.arxiv-vanity.com/papers/quant-ph/0506184/
http://philsci-archive.pitt.edu/814/
http://philsci-archive.pitt.edu/814/1/QSA2001.pdf
http://philsci-archive-dev.library.pitt.edu/814/
https://link.springer.com/content/pdf/10.1023/B:IJTP.0000048813.60909.8c.pdf

Infinite dimensional rotations and Laplacians in terms of white noise calculus

Authors: Hida, Takeyuki, Obata, Nobuaki, Saitô, Kimiaki

Source: Selected Papers of Takeyuki Hida ISBN: 9789810243333
Nagoya Math. J. 128 (1992), 65-93

Subject Terms: second quantized operator, Distributions on infinite-dimensional spaces, creation and annihilation operators on white noise functionals, 46G05, infinite dimensional rotation group, Measures and integration on abstract linear spaces, 58G32, infinite dimensional Laplacians, 01 natural sciences, operators on Fock space, 60J65, integral kernel operator, 46G12, rotation-invariance, 0101 mathematics, 60G20, Gross Laplacian, General theory of partial differential operators, Infinite-dimensional Lie groups and their Lie algebras: general properties, Stochastic analysis, Gelfand triple, Gaussian measure, Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.), number operator, 60H15, 47N30, Brownian motion, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces

File Description: application/xml; application/pdf

Access URL: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/1501AF53442E8F86D4A899ED6E64E59A/S0027763000004220a.pdf/div-class-title-infinite-dimensional-rotations-and-laplacians-in-terms-of-white-noise-calculus-div.pdf
https://projecteuclid.org/journals/nagoya-mathematical-journal/volume-128/issue-none/Infinite-dimensional-rotations-and-Laplacians-in-terms-of-white-noise/nmj/1118783303.pdf
http://ci.nii.ac.jp/naid/110000023363
http://projecteuclid.org/euclid.nmj/1118783303
https://tohoku.pure.elsevier.com/en/publications/infinite-dimensional-rotations-and-laplacians-in-terms-of-white-n
https://www.cambridge.org/core/journals/nagoya-mathematical-journal/article/infinite-dimensional-rotations-and-laplacians-in-terms-of-white-noise-calculus/1501AF53442E8F86D4A899ED6E64E59A
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/1501AF53442E8F86D4A899ED6E64E59A/S0027763000004220a.pdf/div-class-title-infinite-dimensional-rotations-and-laplacians-in-terms-of-white-noise-calculus-div.pdf
https://projecteuclid.org/euclid.nmj/1118783303
http://projecteuclid.org/euclid.nmj/1118783303

Spaces of Test and Generalized Functions Related to Generalized Translation Operators: Spaces of test and generalized functions related to generalized translation operators

Authors: Yu. M. Berezans’kyi, V. A. Tesko

Source: Ukrainian Mathematical Journal. 55:1907-1979

Subject Terms: infinite tensor product, Spaces of differentiable or holomorphic functions on infinite-dimensional spaces, Distributions on infinite-dimensional spaces, Wick multiplication, rigged Hilbert space, Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.), generalized translation operators, 0101 mathematics, White noise theory, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces, 01 natural sciences, Fock space

File Description: application/xml

Access URL: https://zbmath.org/2210389
https://doi.org/10.1023/b:ukma.0000031659.39272.9f
https://link.springer.com/article/10.1023/B%3AUKMA.0000031659.39272.9f
https://imath.kiev.ua/~tesko/pdf/berezansky_tesko_2003%20-%20spaces%20of%20test%20and%20generalized%20functions%20related%20to%20generalized%20translation%20operators.pdf

SUPPORT OF A JOINT RESOLUTION OF IDENTITY AND THE PROJECTION SPECTRAL THEOREM: Support of a joint resolution of identity and the projection spectral theorem

Authors: Pulemyotov, Artem D.

Source: Infinite Dimensional Analysis, Quantum Probability and Related Topics. :549-561

Subject Terms: Spectral theorem, support, Several-variable operator theory (spectral, Fredholm, etc.), 4. Education, Joint resolution of identity, joint resolution of identity, Generalized eigenvector, 16. Peace & justice, 01 natural sciences, projection spectral theorem, generalized eigenvector, Spectrum, resolvent, 0101 mathematics, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces

File Description: application/xml

Access URL: https://espace.library.uq.edu.au/view/UQ:283592
https://www.worldscientific.com/doi/abs/10.1142/S0219025703001444

Lax-Phillips evolutions in quantum mechanics and two-space scattering: Lax--Phillips evolutions in quantum mechanics and two-space scattering.

Authors: Baumgärtel, Hellmut

Source: Reports on Mathematical Physics. 52:295-307

Subject Terms: Lax--Phillips evolution, Applications of operator theory in the physical sciences, Scattering theory of linear operators, 0103 physical sciences, Institut für Physik und Astronomie, canonical extensions of Hamiltonians, 0101 mathematics, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces, 01 natural sciences, 2-space scattering, \(S\)-matrix theory, etc. in quantum theory

File Description: application/xml

Access URL: https://zbmath.org/2084230
https://doi.org/10.1016/s0034-4877(03)90018-8
http://ui.adsabs.harvard.edu/abs/2003RpMP...52..295B/abstract
https://www.sciencedirect.com/science/article/pii/S0034487703900188
https://publishup.uni-potsdam.de/frontdoor/index/index/docId/14569
https://publishup.uni-potsdam.de/frontdoor/index/index/docId/14403

Resonances in the Rigged Hilbert Space and Lax-Phillips Scattering Theory: Resonances in the rigged Hilbert space and Lax-Phillips scattering theory

Authors: Y. Strauss

Source: International Journal of Theoretical Physics. 42:2285-2315

Subject Terms: \(2\)-body potential quantum scattering theory, Scattering theory of linear operators, Applications of operator theory in the physical sciences, Lax-Philips scattering theory, Quantum scattering theory, Hardy space, 01 natural sciences, resonance, Toeplitz operator, rigged Hilbert space, Banach spaces of continuous, differentiable or analytic functions, 0103 physical sciences, semigroup evolution, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems

File Description: application/xml

Access URL: https://zbmath.org/2036945
https://link.springer.com/article/10.1023%2FB%3AIJTP.0000005959.97056.8b
http://ui.adsabs.harvard.edu/abs/2003IJTP...42.2285S/abstract
https://link.springer.com/content/pdf/10.1023/B:IJTP.0000005959.97056.8b.pdf

The Generalized Moment Problem Associated with Correlation Measures: The generalized moment problem associated with correlation measures.

Authors: Yu. M. Berezansky

Source: Functional Analysis and Its Applications. 37:311-315

Subject Terms: Linear symmetric and selfadjoint operators (unbounded), correlation measure, Partial differential equations on manifolds, differential operators, Measures of association (correlation, canonical correlation, etc.), positive functional, convolution, generalized joint eigenvector, Quantum equilibrium statistical mechanics (general), 0101 mathematics, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces, 01 natural sciences, Applications of operator theory in statistical physics, Operations with distributions and generalized functions

File Description: application/xml

Access URL: https://zbmath.org/2138548
https://doi.org/10.1023/b:faia.0000015580.92172.6c
https://link.springer.com/article/10.1023/B:FAIA.0000015581.58381.a0
https://link.springer.com/content/pdf/10.1023/B:FAIA.0000015581.58381.a0.pdf

On 1–dimensional dissipative Schrödinger–type operators their dilations and eigenfunction expansions: On 1-dimensional dissipative Schrödinger-type operators their dilations and eigenfunction expansions

Authors: Rehberg, Joachim, Neidhardt, Hagen, Kaiser, Hans-Christoph

Source: Mathematische Nachrichten. 252:51-69

Subject Terms: ddc:510, dissipative Schrödinger-type operators -- Sturm-Liouville operators -- characteristic function -- minimal dilation -- eigenfunction expansion, article, General theory of ordinary differential operators, Sturm-Liouville operators, resolvent, dissipative boundary conditions, non-selfadjointness, Linear accretive operators, dissipative operators, etc, generalized eigenfunction expansion, 01 natural sciences, characteristic function, Dissipative Schrödinger-type operators, one-dimensional Schrödinger-type operators, dilation, 0101 mathematics, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces

File Description: application/xml

Access URL: http://onlinelibrary.wiley.com/doi/10.1002/mana.200310037/pdf

Riesz basis property of Timoshenko beams with boundary feedbackcontrol: Riesz basis property of Timoshenko beams with boundary feedback control

Authors: Feng, DX, Yung, SP, Xu, GQ

Source: International Journal of Mathematics and Mathematical Sciences, Vol 2003, Iss 28, Pp 1807-1820 (2003)

Subject Terms: One-parameter semigroups and linear evolution equations, Control/observation systems governed by partial differential equations, \(C_0\)-semigroups, exponential decay, Feedback control, Linear accretive operators, dissipative operators, etc, 01 natural sciences, Higher-order hyperbolic systems, QA1-939, Rods (beams, columns, shafts, arches, rings, etc.), Initial-boundary value problems for second-order hyperbolic equations, 0101 mathematics, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces, Mathematics

File Description: application/xml

Access URL: https://downloads.hindawi.com/journals/ijmms/2003/602015.pdf
https://zbmath.org/1930068
https://doi.org/10.1155/s0161171203011414
https://doaj.org/article/3aa02d14ca294af7874ac47406067250
https://hub.hku.hk/handle/10722/53391
http://hub.hku.hk/bitstream/10722/53391/1/79181.pdf
http://emis.math.tifr.res.in/journals/HOA/IJMMS/2003/281807.pdf
http://emis.maths.adelaide.edu.au/journals/HOA/IJMMS/Volume2003_28/1820.pdf
https://downloads.hindawi.com/journals/ijmms/2003/602015.pdf
https://www.emis.de/journals/HOA/IJMMS/Volume2003_28/602015.pdf
http://hdl.handle.net/10722/53391