Fractional calculus for distributions

Authors: Hilfer, Rudolf, Kleiner, Tillmann

Source: Fractional Calculus and Applied Analysis. 27:2063-2123

Subject Terms: General integral transforms, distributions, fractional calculus, 01 natural sciences, Operations with distributions and generalized functions, Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures, Fractional derivatives and integrals, Classical operational calculus, Integral transforms in distribution spaces, convolution, 0101 mathematics

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Access URL: https://zbmath.org/7988569
https://doi.org/10.1007/s13540-024-00306-z
https://elib.uni-stuttgart.de/handle/11682/16600
http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-166000
https://doi.org/10.18419/opus-16581

A Unified Approach to Time–Frequency Representations and Generalized Spectrograms: A unified approach to time-frequency representations and generalized spectrograms

Authors: Elena Cordero, Gianluca Giacchi, Luigi Rodino

Source: Journal of Fourier Analysis and Applications. 31

Subject Terms: Time–frequency analysis, Spectrogram, Short-time Fourier transform, Wigner distribution, Cohen's class, Signal theory (characterization, reconstruction, filtering, etc.), Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics, time-frequency analysis, Cohen's class, Short-time Fourier transform, Spectrogram, Time–frequency analysis, Wigner distribution, Operations with distributions and generalized functions, Mathematics - Analysis of PDEs, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, spectrogram, short-time Fourier transform, Integral transforms in distribution spaces, 42A38, 46F10, 46F12, 81S30

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Access URL: http://arxiv.org/abs/2401.03882
https://zbmath.org/8034231
https://doi.org/10.1007/s00041-024-10142-7
https://link.springer.com/article/10.1007/s00041-024-10142-7
https://hdl.handle.net/11585/1003061
https://doi.org/10.1007/s00041-024-10142-7
https://hdl.handle.net/2318/2067190
https://link-springer-com.bibliopass.unito.it/article/10.1007/s00041-024-10142-7
https://doi.org/10.1007/s00041-024-10142-7

Linear canonical wavelet transform and linear canonical wave packet transform on the Schwartz type spaces

Authors: M. Thanga Rejini, R. Subash Moorthy

Source: The Journal of Analysis. 33:455-479

Subject Terms: linear canonical transform, tempered distributions, wave packet transform, Topological linear spaces of test functions, distributions and ultradistributions, Schwartz space, Integral transforms in distribution spaces, canonical wavelet, Operations with distributions and generalized functions

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Access URL: https://zbmath.org/8035905
https://doi.org/10.1007/s41478-023-00673-5

The continuous quaternion wavelet transform on distribution spaces

Authors: Drema Lhamu, Aparna Das, Sunil Kumar Singh, Awniya Kumar

Source: Rendiconti del Circolo Matematico di Palermo Series 2. 74

Subject Terms: quaternions, continuous quaternion wavelet transform, Besov spaces and \(Q_p\)-spaces, Integral transforms in distribution spaces, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, Sobolev space, Besov space

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Access URL: https://zbmath.org/7971729
https://doi.org/10.1007/s12215-024-01180-7

A result on the neutrix convolution product of distributions

Authors: Fisher, Brian

Source: Publicationes Mathematicae Debrecen. 37:267-271

Subject Terms: neutrix calculus, Integral transforms in distribution spaces, 0101 mathematics, convolution product, 01 natural sciences, Operations with distributions and generalized functions

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Access URL: https://zbmath.org/9557

Operational calculus on a subset of $R^n$: Operational calculus on a subset of \(R^ n\)

Authors: Shultz, Harris S.

Source: Publicationes Mathematicae Debrecen. 34:105-108

Subject Terms: Convolution as an integral transform, Classical operational calculus, Integral transforms in distribution spaces, test functions, convolution, operational formulas, 0101 mathematics, algebra of operators, 01 natural sciences

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Access URL: https://zbmath.org/4015395

On extremal domains and codomains for convolution of distributions and fractional calculus

Authors: Kleiner, T., Hilfer, R.

Source: Monatshefte für Mathematik. 198:121-152

Subject Terms: quantales, fractional calculus, spaces of distributions, 01 natural sciences, Operations with distributions and generalized functions, Convolution as an integral transform, General theory of locally convex spaces, Fractional derivatives and integrals, Quantales, Integral transforms in distribution spaces, convolution, 0101 mathematics

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Access URL: https://link.springer.com/content/pdf/10.1007/s00605-021-01646-1.pdf

Generalized pseudo-differential operators associated with symbol classes involving fractional Fourier transform

Authors: Shekhar, Abhisekh, Agrawal, Nawin Kumar

Source: Serdica Mathematical Journal. 48

Subject Terms: pseudo-differential operators, Topological linear spaces of test functions, distributions and ultradistributions, Pseudodifferential operators as generalizations of partial differential operators, Integral transforms in distribution spaces, symbol classes, tempered distribution, Topological linear spaces of continuous, differentiable or analytic functions, Pseudodifferential operators, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, fractional Fourier transform, Sobolev space

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Access URL: https://zbmath.org/8019405
https://doi.org/10.55630/serdica.2022.48.247-270

A framework of linear canonical Hankel transform pairs in distribution spaces and their applications

Authors: Srivastava, H. M.^{Aff1, Aff2, Aff3, Aff4, IDs13398021011134_cor1}, Kumar, Manish, Pradhan, Tusharakanta

Source: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 115(4)

Generalized Functions in Signal Theory: Generalized functions in signal theory

Authors: Jondral, Friedrich

Source: Recent Developments in Infinite-Dimensional Analysis and Quantum Probability ISBN: 9789401038423

Subject Terms: ddc:620, Signal theory (characterization, reconstruction, filtering, etc.), generalized functions, 4. Education, Generalized stochastic processes, 16. Peace & justice, signal theory, transmission function, General second-order stochastic processes, Integral transforms in distribution spaces, impulse response, bandlimited signals, white noise, Engineering & allied operations

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Access URL: https://zbmath.org/1621305
https://doi.org/10.1023/a:1010711420103
https://rd.springer.com/chapter/10.1007/978-94-010-0842-6_12
https://link.springer.com/chapter/10.1007/978-94-010-0842-6_12
https://link.springer.com/content/pdf/10.1007%2F978-94-010-0842-6_12.pdf

Injectivity sets of the Pompeiu transform

Authors: Vit. V. Volchkov

Source: Integral Geometry and Convolution Equations ISBN: 9789401039994

Subject Terms: distributions with support on the unit sphere, injectivity sets of the Pompeiu transform, Integral transforms in distribution spaces, Integral geometry, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/1428709
https://doi.org/10.1070/sm1999v190n11abeh000439
http://ui.adsabs.harvard.edu/abs/1999SbMat.190.1607V/abstract
https://link.springer.com/content/pdf/10.1007%2F978-94-010-0023-9_25.pdf
https://rd.springer.com/chapter/10.1007/978-94-010-0023-9_25
https://link.springer.com/chapter/10.1007/978-94-010-0023-9_25
http://www.osti.gov/scitech/biblio/21202895-injectivity-sets-pompeiu-transform
http://iopscience.iop.org/article/10.1070/SM1999v190n11ABEH000439/pdf

Fourier transformation of Sato's hyperfunctions

Authors: A. G. Smirnov

Source: Advances in Mathematics. 196:310-345

Subject Terms: Mathematics(all), Distributions and ultradistributions as boundary values of analytic functions, Mathematics - Complex Variables, Hyperfunctions, analytic functionals, Analytic functionals, 01 natural sciences, 32A45, Functional Analysis (math.FA), Mathematics - Functional Analysis, Fourier transformation, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, 0103 physical sciences, FOS: Mathematics, Integral transforms in distribution spaces, Gelfand-Shilov classes, ultrafunctionals, 46F15, Complex Variables (math.CV), 0101 mathematics, weighted inductive limit of entire functions, Hyperfunctions

File Description: application/xml

Access URL: http://arxiv.org/abs/math/0401151
https://zbmath.org/2213017
https://doi.org/10.1016/j.aim.2004.09.003
https://www.sciencedirect.com/science/article/abs/pii/S0001870804002889
https://dialnet.unirioja.es/servlet/articulo?codigo=1275722
https://core.ac.uk/display/82788998
http://www.sciencedirect.com/science/article/pii/S0001870804002889
https://www.sciencedirect.com/science/article/pii/S0001870804002889

Poisson kernels and sparse wavelet expansions

Authors: Lorenzo Brandolese

Source: Proceedings of the American Mathematical Society. 133:3345-3353

Subject Terms: Besov spaces, Integral transforms in distribution spaces, tempered distribution, Nontrigonometric harmonic analysis involving wavelets and other special systems, 0101 mathematics, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, 01 natural sciences, wavelet expansions, nonlinear approximation

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Access URL: https://www.ams.org/proc/2005-133-11/S0002-9939-05-07893-7/S0002-9939-05-07893-7.pdf
https://www.ams.org/journals/proc/2005-133-11/S0002-9939-05-07893-7/home.html
https://dialnet.unirioja.es/servlet/articulo?codigo=1376733
https://www.ams.org/proc/2005-133-11/S0002-9939-05-07893-7/S0002-9939-05-07893-7.pdf

Hankel Convolution Operators on Spaces of Entire Functions of Finite Order: Hankel convolution operators on spaces of entire functions of finite order

Authors: Jorge J. Betancor

Source: Canadian Mathematical Bulletin. 48:161-174

Subject Terms: 0301 basic medicine, 03 medical and health sciences, finite order, 13. Climate action, Topological linear spaces of test functions, distributions and ultradistributions, entire function, Integral transforms in distribution spaces, convolution, 0101 mathematics, 16. Peace & justice, 01 natural sciences, Hankel transformation

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Access URL: https://documat.unirioja.es/servlet/articulo?codigo=1173215
https://dialnet.unirioja.es/servlet/articulo?codigo=1173215

On the surjectivity of Hankel convolution operators on Beurling-type distribution spaces

Authors: M. Belhadj, J. J. Betancor

Source: Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 135:479-512

Subject Terms: Hankel convolution operator, Integral transforms in distribution spaces, 0101 mathematics, Hankel transform, 01 natural sciences, Operations with distributions and generalized functions

File Description: application/xml

Access URL: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0308210500003978
http://www.journals.cambridge.org/abstract_S0308210500003978

Chordal Loewner families and univalent Cauchy transforms

Authors: Robert O. Bauer

Source: Journal of Mathematical Analysis and Applications. 302:484-501

Subject Terms: Mathematics - Complex Variables, Applied Mathematics, Probability (math.PR), General theory of univalent and multivalent functions of one complex variable, 30C45, 30E20, 60E10, 01 natural sciences, FOS: Mathematics, Integral transforms in distribution spaces, Complex Variables (math.CV), 0101 mathematics, Analysis, Mathematics - Probability

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Access URL: http://arxiv.org/abs/math/0306130
https://www.sciencedirect.com/science/article/abs/pii/S0022247X04006663
http://ui.adsabs.harvard.edu/abs/2003math......6130B/abstract
https://experts.illinois.edu/en/publications/chordal-loewner-families-and-univalent-cauchy-transforms
https://www.sciencedirect.com/science/article/pii/S0022247X04006663
https://core.ac.uk/display/82722537

Stability Estimates for Helical Computer Tomography: Stability estimates for helical computer tomography

Authors: Katsevich, Alexander

Source: Journal of Fourier Analysis and Applications. 11:85-105

Subject Terms: helical tomography, cone-beam, 01 natural sciences, inversion, RADON TRANSFORMS, Stability estimates, RECONSTRUCTION, ALGORITHM, 0101 mathematics, Helical tomography, Microlocal analysis, Radon transform, Biomedical imaging and signal processing, 4. Education, Inversion, X-RAY TRANSFORM, extension to distributions, CONE-BEAM TOMOGRAPHY, microlocal analysis, stability estimates, Sobolev spaces, Applied, Integral transforms in distribution spaces, Extension to distributions, Mathematics, Cone-beam

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Access URL: https://link.springer.com/article/10.1007/s00041-004-4013-6

On a Regularization Scheme for Linear Operators in Distribution Spaces with an Application to the Spherical Radon Transform: On a regularization scheme for linear operators in distribution spaces with an application to the spherical Radon transform

Authors: Thomas Schuster, Eric Todd Quinto

Source: SIAM Journal on Applied Mathematics. 65:1369-1387

Subject Terms: Hilbert spaces, spherical Radon transform, numerical results, reconstruction kernel, sonar, 01 natural sciences, regularization, approximate inverse, mollifier, Numerical solutions to equations with linear operators, distribution, Integral transforms in distribution spaces, 0101 mathematics, Numerical methods for integral transforms, Equations and inequalities involving linear operators, with vector unknowns, Radon transform, linear operator equation

File Description: application/xml

Access URL: https://publikationen.sulb.uni-saarland.de/bitstream/20.500.11880/26317/1/preprint_109_04.pdf
https://publikationen.sulb.uni-saarland.de/handle/20.500.11880/26317
http://scidok.sulb.uni-saarland.de/volltexte/2012/4466/
https://epubs.siam.org/doi/10.1137/S003613990343879X
https://dblp.uni-trier.de/db/journals/siamam/siamam65.html#SchusterQ05
https://doi.org/10.1137/S003613990343879X

Operational calculus and Fourier transform on Boehmians

Authors: R. Roopkumar, V. Karunakaran

Source: Colloquium Mathematicum. 102:21-32

Subject Terms: generalized product, ultradistributions, Integral transforms of special functions, Classical operational calculus, Fourier transform, Integral transforms in distribution spaces, Boehmians, 0101 mathematics, 01 natural sciences

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Access URL: https://www.impan.pl/shop/publication/transaction/download/product/86887?download.pdf
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-1-3
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/colloquium-mathematicum/all/102/1/86887/operational-calculus-and-fourier-transform-on-boehmians
https://eudml.org/similar/doc/283933

Characterization of Functions with Fourier Transform Supported on Orthants: Characterization of functions with Fourier transform supported on orthants

Authors: J. N. Pandey, O. P. Singh

Source: Generalized Functions and Their Applications ISBN: 9781489915931

Subject Terms: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Applied Mathematics, distributions, Schwartz space, Fourier transform, Integral transforms in distribution spaces, 0101 mathematics, 01 natural sciences, Analysis, orthants

File Description: application/xml

Access URL: https://zbmath.org/663698
https://doi.org/10.1006/jmaa.1994.1260
https://www.sciencedirect.com/science/article/pii/S0022247X84712601
https://rd.springer.com/chapter/10.1007/978-1-4899-1591-7_16
https://core.ac.uk/display/82087147
https://link.springer.com/chapter/10.1007/978-1-4899-1591-7_16
http://www.sciencedirect.com/science/article/pii/S0022247X84712601