Analytic Fourier Transforms and Exponential Approximations. II: Analytic Fourier transforms and exponential approximations. II

Authors: A. M. Sedletskii

Source: Journal of Mathematical Sciences. 130:5083-5255

Subject Terms: nonharmonic Fourier series, shift approximation, Laplace transform, Completeness of sets of functions in one variable harmonic analysis, analyticity, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), 01 natural sciences, bases of exponents, rapidly decreasing function, completeness, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Fourier transform, 0101 mathematics, minimality, Completeness of sets of functions in nontrigonometric harmonic analysis, Müntz-Szasz approximation

File Description: application/xml

Access URL: https://link.springer.com/10.1007/s10958-005-0397-3
https://link.springer.com/article/10.1007%2Fs10958-005-0349-y

Backward adaptive biorthogonalization

Authors: Laura Rebollo-Neira

Source: International Journal of Mathematics and Mathematical Sciences, Vol 2004, Iss 35, Pp 1843-1853 (2004)

Subject Terms: orthogonal projections, FOS: Physical sciences, Completeness of sets of functions in one variable harmonic analysis, Mathematical Physics (math-ph), 02 engineering and technology, backward biorthogonalization, 01 natural sciences, Functional Analysis (math.FA), Mathematics - Functional Analysis, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), 0103 physical sciences, QA1-939, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, Linear function spaces and their duals, Mathematics, Completeness of sets of functions in nontrigonometric harmonic analysis, Mathematical Physics

File Description: application/xml

Access URL: http://downloads.hindawi.com/journals/ijmms/2004/701068.pdf
http://arxiv.org/abs/math-ph/0211066
https://doaj.org/article/ab731f701d57465ea9af7923aeb77f5e
https://www.emis.de/journals/HOA/IJMMS/Volume2004_35/1853.pdf
https://dblp.uni-trier.de/db/journals/ijmmsc/ijmmsc2004.html#Rebollo-Neira04
https://www.hindawi.com/journals/ijmms/2004/701068/
https://downloads.hindawi.com/journals/ijmms/2004/701068.pdf

Almost Integer Translates. Do Nice Generators Exist?: Almost integer translates. Do nice generators exist?

Authors: Alexander Olevskii, Alexander Ulanovskii

Source: Journal of Fourier Analysis and Applications. 10:93-104

Subject Terms: system of translates, weighted spaces, Completeness of sets of functions in one variable harmonic analysis, 0101 mathematics, generators, 01 natural sciences, Completeness of sets of functions in nontrigonometric harmonic analysis

File Description: application/xml

Access URL: https://zbmath.org/2105069
https://doi.org/10.1007/s00041-004-8006-2
https://link.springer.com/article/10.1007/s00041-004-8006-2
https://link.springer.com/10.1007/s00041-004-8006-2
https://dialnet.unirioja.es/servlet/articulo?codigo=882551

unconditional bases the matrix muckenhoupt condition and carleson series in a spectrum: Unconditional bases, the matrix Muckenhoupt condition and Carleson series in a spectrum

Authors: E. I. Olefir, G. M. Gubreev

Source: Journal of Mathematical Sciences. 110(5):2955-2978

Subject Terms: rational vector-valued functions, Hilbert transform of vector-valued functions, Summability and bases, functional analytic aspects of frames in Banach and Hilbert spaces, Completeness of sets of functions in one variable harmonic analysis, spectral structure, Carleson series, integration operators, finite system of scalar Muckenhoupt weights, perturbations, unconditional bases, Banach spaces of continuous, differentiable or analytic functions, Linear operators on function spaces (general), two-sided estimates, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces

File Description: application/xml

Access URL: https://zbmath.org/1777262
https://doi.org/10.1023/a:1015335220037
https://link.springer.com/article/10.1023%2FA%3A1015335220037

Unconditional Bases, the Matrix Muckenhoupt Condition, and Carleson Series in a Spectrum: Unconditional bases, the matrix Muckenhoupt condition and Carleson series in a spectrum

Authors: E. I. Olefir, G. M. Gubreev

Source: Journal of Mathematical Sciences. 110:2955-2978

Subject Terms: rational vector-valued functions, Hilbert transform of vector-valued functions, Summability and bases, functional analytic aspects of frames in Banach and Hilbert spaces, Completeness of sets of functions in one variable harmonic analysis, spectral structure, Carleson series, integration operators, 01 natural sciences, finite system of scalar Muckenhoupt weights, perturbations, unconditional bases, Banach spaces of continuous, differentiable or analytic functions, Linear operators on function spaces (general), two-sided estimates, 0101 mathematics, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces

File Description: application/xml

Access URL: https://zbmath.org/1777262
https://doi.org/10.1023/a:1015335220037
https://link.springer.com/article/10.1023%2FA%3A1015335220037

On the order of the best approximation in spaces with asymmetric norm and sign-sensitive weight on classes of differentiable functions: On the order of the best approximation in spaces with asymmetric norm and sign-sensitive weight on classes of differentiable functions.

Authors: A. I. Kozko

Source: Izvestiya: Mathematics. 66:103-131

Subject Terms: Trigonometric approximation, trigonometric polynomials, 0211 other engineering and technologies, trigonometric approximation, Rate of convergence, degree of approximation, Completeness of sets of functions in one variable harmonic analysis, 02 engineering and technology, 01 natural sciences, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Approximation with constraints, degree of approximation, 0101 mathematics, asymmetric norms, best approximation, rate of convergence

File Description: application/xml

Access URL: https://zbmath.org/1902121
https://doi.org/10.1070/im2002v066n01abeh000373
https://istina.msu.ru/publications/article/11229951/
https://iopscience.iop.org/article/10.1070/IM2002v066n01ABEH000373/meta
https://ui.adsabs.harvard.edu/abs/2002IzMat..66..103K/abstract

Perturbation of orthonormal bases inL 2-spaces: Perturbation of orthonormal bases in \(L^2\)-spaces

Authors: Xionghui He, Eric S. Key, Hans Volkmer

Source: Integral Equations and Operator Theory. 41:396-409

Subject Terms: Sturm-Liouville differential operator, perturbation, Completeness of sets of functions in one variable harmonic analysis, Nontrigonometric harmonic analysis involving wavelets and other special systems, Riesz bases, 0101 mathematics, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, 01 natural sciences, Completeness of sets of functions in nontrigonometric harmonic analysis

File Description: application/xml

Access URL: https://zbmath.org/1694213
https://doi.org/10.1007/bf01202101
https://link.springer.com/article/10.1007/BF01202101

Completeness of Trigonometric System with Integer Indices {e;x∈ }: Completeness of trigonometric system with integer indices \(\{ e^{inx};x\in\Re\}\)

Authors: Akio Arimoto

Source: Journal of Approximation Theory. 112:311-317

Subject Terms: Mathematics(all), Numerical Analysis, completeness, Applied Mathematics, trigonometric systems, Completeness of sets of functions in one variable harmonic analysis, 0101 mathematics, 01 natural sciences, Analysis

File Description: application/xml

Access URL: https://zbmath.org/1722134
https://doi.org/10.1006/jath.2001.3591
https://dblp.uni-trier.de/db/journals/jat/jat112.html#Arimoto01
https://www.sciencedirect.com/science/article/pii/S0021904501935919
https://core.ac.uk/display/82491146
http://www.sciencedirect.com/science/article/pii/S0021904501935919

On completeness of random exponentials in the Bargmann–Fock space: On completeness of random exponentials in the Bargmann-Fock space

Authors: Leonid Pastur, Yu. Lyubarskii, G. P. Chistyakov

Source: Journal of Mathematical Physics. 42:3754-3768

Subject Terms: ergodic point field, completeness, Bargmann-Fock space, 0103 physical sciences, Completeness of sets of functions in one variable harmonic analysis, random exponentials, 0101 mathematics, system of exponentials, 01 natural sciences, Probabilistic methods for one variable harmonic analysis, Completeness problems, closure of a system of functions of one complex variable, Commutation relations and statistics as related to quantum mechanics (general)

File Description: application/xml

Access URL: https://zbmath.org/1711430
https://doi.org/10.1063/1.1379311
http://ui.adsabs.harvard.edu/abs/2001JMP....42.3754C/abstract
https://aip.scitation.org/doi/10.1063/1.1379311

An Exactly Solvable Model for the Interaction of Linear Waves with Korteweg--de Vries Solitons: An exactly solvable model for the interaction of linear waves with Korteweg--de Vries solitons

Authors: Peter D. Miller, Simon R Clarke

Source: SIAM Journal on Mathematical Analysis. 33:261-285

Subject Terms: Soliton equations, Nonlinear Sciences - Exactly Solvable and Integrable Systems, wave trapping, FOS: Physical sciences, Completeness of sets of functions in one variable harmonic analysis, coupled systems, Pattern Formation and Solitons (nlin.PS), Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems, Nonlinear Sciences - Pattern Formation and Solitons, 01 natural sciences, KdV equations (Korteweg-de Vries equations), Korteweg-de Vries equation, 0103 physical sciences, solitons, Exactly Solvable and Integrable Systems (nlin.SI), completeness relations

File Description: application/xml

Access URL: http://www.math.lsa.umich.edu/~millerpd/docs/J25.pdf
http://arxiv.org/abs/nlin/0101027
https://zbmath.org/1670350
https://doi.org/10.1137/s0036141099365431
http://www.math.lsa.umich.edu/~millerpd/docs/J25.pdf
https://research.monash.edu/en/publications/an-exactly-solvable-model-for-the-interaction-of-linear-waves-wit
https://dblp.uni-trier.de/db/journals/siamma/siamma33.html#MillerC01
https://epubs.siam.org/doi/abs/10.1137/S0036141099365431
http://doi.org/10.1137/S0036141099365431
https://doi.org/10.1137/S0036141099365431

Nonperiodic sampling and the local three squares theorem

Authors: Gröchenig, Karlheinz, Heil, Christopher, Walnut, David

Source: Ark. Mat. 38, no. 1 (2000), 77-92

Subject Terms: 1010 Mathematics, Trigonometric moment problems in one variable harmonic analysis, Pompeiu problems, 1010 Mathematik, exact sequences, Switching theory, application of Boolean algebra, Boolean functions, irregular sampling, Completeness of sets of functions in one variable harmonic analysis, Nontrigonometric harmonic analysis involving wavelets and other special systems, three squares theorem, 0101 mathematics, 01 natural sciences, nonperiodic sampling

File Description: application/xml; application/pdf

Access URL: https://ucrisportal.univie.ac.at/de/publications/ba89aa17-bbec-49cf-8fe3-6b95c09f18c4
http://ui.adsabs.harvard.edu/abs/2000ArM....38...77G/abstract
https://link.springer.com/content/pdf/10.1007/BF02384491.pdf
https://projecteuclid.org/euclid.afm/1485898667
https://link.springer.com/article/10.1007/BF02384491
http://projecteuclid.org/euclid.afm/1485898667

On Gröchenig, Heil, and Walnut's proof of the local three squares theorem

Authors: Seip, Kristian

Source: Ark. Mat. 38, no. 1 (2000), 93-96

Subject Terms: completeness, 0202 electrical engineering, electronic engineering, information engineering, Completeness of sets of functions in one variable harmonic analysis, General harmonic expansions, frames, 02 engineering and technology, 0101 mathematics, locl three squares theorem, 01 natural sciences

File Description: application/xml; application/pdf

Access URL: https://link.springer.com/article/10.1007/BF02384492
https://projecteuclid.org/download/pdf_1/euclid.afm/1485898668
https://projecteuclid.org/journals/arkiv-for-matematik/volume-38/issue-1/On-Gr%C3%B6chenig-Heil-and-Walnuts-proof-of-the-local-three/10.1007/BF02384492.full
https://ui.adsabs.harvard.edu/abs/2000ArM....38...93S/abstract
http://projecteuclid.org/euclid.afm/1485898668

Fourier bases and a distance problem of Erd\H os: Fourier bases and a distance problem of Erdős

Authors: Steen Pedersen, Nets Hawk Katz, Alex Iosevich

Source: Mathematical Research Letters. 6:251-255

Subject Terms: Mathematics - Classical Analysis and ODEs, number of distances, non-harmonic orthogonal basis of exponentials, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Completeness of sets of functions in one variable harmonic analysis, conjecture of Fuglede, 0101 mathematics, 01 natural sciences, Erdős problems and related topics of discrete geometry, Completeness of sets of functions in nontrigonometric harmonic analysis

File Description: application/xml

Access URL: http://www.intlpress.com/site/pub/files/_fulltext/journals/mrl/1999/0006/0002/MRL-1999-0006-0002-a013.pdf
http://arxiv.org/abs/math/0104092
https://www.intlpress.com/site/pub/files/_fulltext/journals/mrl/1999/0006/0002/MRL-1999-0006-0002-a013.pdf
https://www.intlpress.com/site/pub/pages/journals/items/mrl/content/vols/0006/0002/a013/

Systems with nonextendable convergence of quasipolynomials

Authors: A. A. Ryabinin

Source: Mathematical Notes. 64:629-633

Subject Terms: singular Cantor-Lebesgue measure, convergence, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, 0103 physical sciences, Fourier transform, Completeness of sets of functions in one variable harmonic analysis, quasipolynomials, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/1407582
https://doi.org/10.1007/bf02316288
https://link.springer.com/article/10.1007/BF02316288
https://link.springer.com/content/pdf/10.1007/BF02316288.pdf

On the Completeness and Other Properties of Some Function Systems inL, 0

Authors: Vadim I Filippov

Source: Journal of Approximation Theory. 94:42-53

Subject Terms: Mathematics(all), Numerical Analysis, completeness, Applied Mathematics, Summability and bases, functional analytic aspects of frames in Banach and Hilbert spaces, Completeness of sets of functions in one variable harmonic analysis, 0101 mathematics, 01 natural sciences, representation system, Analysis, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

File Description: application/xml

Access URL: https://zbmath.org/1214031
https://doi.org/10.1006/jath.1998.3176
https://core.ac.uk/display/82306721
https://www.sciencedirect.com/science/article/abs/pii/S0021904598931768
https://www.sciencedirect.com/science/article/pii/S0021904598931768

An Optimal Interpolation Theorem of Marcinkiewicz Type in Orlicz Spaces: An optimal interpolation theorem of Marcinkiewicz type in Orlicz spaces

Authors: CIANCHI, ANDREA

Source: Journal of Functional Analysis. 153:357-381

Subject Terms: Marcinkiewicz weak interpolation theorem, Orlicz function, Interpolation, Orlicz paces, quasilinear operators, Abstract interpolation of topological vector spaces, Completeness of sets of functions in one variable harmonic analysis, Applications of functional analysis to differential and integral equations, Orlicz spaces, 0101 mathematics, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, 01 natural sciences, Analysis, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

File Description: application/xml

Access URL: https://zbmath.org/1215689
https://doi.org/10.1006/jfan.1997.3193
https://www.sciencedirect.com/science/article/pii/S0022123697931931
https://core.ac.uk/display/82586865
http://www.sciencedirect.com/science/article/pii/S0022123697931931
https://hdl.handle.net/2158/204780

Fundamental sets of functions on spheres

Authors: Valdir Antônio Menegatto

Source: Methods and Applications of Analysis. 5:387-398

Subject Terms: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), Approximation by arbitrary linear expressions, Multidimensional problems, 0211 other engineering and technologies, Positive definite functions in one variable harmonic analysis, Completeness of sets of functions in one variable harmonic analysis, 02 engineering and technology, 0101 mathematics, 01 natural sciences, Approximation by other special function classes, Completeness of sets of functions in nontrigonometric harmonic analysis

File Description: application/xml

Access URL: http://www.intlpress.com/site/pub/files/_fulltext/journals/maa/1998/0005/0004/MAA-1998-0005-0004-a004.pdf
https://zbmath.org/1310569
https://doi.org/10.4310/maa.1998.v5.n4.a4
https://www.intlpress.com/site/pub/files/_fulltext/journals/maa/1998/0005/0004/MAA-1998-0005-0004-a004.pdf

On a theorem of Ingham

Authors: Jaffard, S., Tucsnak, M., Zuazua, E.

Source: The Journal of Fourier Analysis and Applications. 3:577-582

Subject Terms: nonharmonic Fourier series, control of PDEs, Classical almost periodic functions, mean periodic functions, Completeness of sets of functions in one variable harmonic analysis, Nontrigonometric harmonic analysis involving wavelets and other special systems, Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization, Existence theories for optimal control problems involving partial differential equations, 16. Peace & justice, 01 natural sciences, Article, Riesz basis, 510.mathematics, Spline approximation, spline functions, 0103 physical sciences, 0101 mathematics

File Description: application/xml; image/jpeg; application/pdf

Access URL: https://zbmath.org/1103022
https://doi.org/10.1007/bf02648885
https://link.springer.com/article/10.1007/BF02648885
https://eudml.org/doc/59526

Sampling multipliers and the Poisson Summation Formula: Sampling multipliers and the Poisson summation formula

Authors: Bendedetto, John J., Zimmerman, Georg

Source: The Journal of Fourier Analysis and Applications. 3:505-523

Subject Terms: 4. Education, Completeness of sets of functions in one variable harmonic analysis, Poisson summation formula, General harmonic expansions, frames, 02 engineering and technology, 16. Peace & justice, Multipliers in one variable harmonic analysis, 01 natural sciences, Article, periodization, 510.mathematics, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, sampling operators, sampling multipliers, Fourier transform, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics

File Description: application/xml; image/jpeg; application/pdf

Access URL: https://link.springer.com/article/10.1007/BF02648881

Fundamental sets of continuous functions on spheres

Authors: Xingping Sun, E. W. Cheney

Source: Constructive Approximation. 13:245-250

Subject Terms: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), Approximation by arbitrary linear expressions, Multidimensional problems, Positive definite functions in one variable harmonic analysis, fundamental sets of continuous functions, Completeness of sets of functions in one variable harmonic analysis, 0101 mathematics, 01 natural sciences, Approximation by other special function classes, Completeness of sets of functions in nontrigonometric harmonic analysis

File Description: application/xml

Access URL: https://zbmath.org/1023012
https://doi.org/10.1007/bf02678466
https://link.springer.com/article/10.1007/BF02678466
https://bearworks.missouristate.edu/articles-cnas/2658/