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

File Description: application/xml; application/pdf

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 Distributional Version of the Ferenc Lukács Theorem: A distributional version of the Ferenc Lukács theorem

Authors: Estrada, Ricardo

Source: Sarajevo Journal of Mathematics. 1:75-92

Subject Terms: Fourier coefficients, Fourier series of functions with special properties, special Fourier series, Conjugate functions, conjugate series, singular integrals, Abel-Poisson means, periodic distributions, conjugate Fourier series, Operations with distributions and generalized functions

File Description: application/xml

Access URL: https://zbmath.org/2166224

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

File Description: application/xml; application/pdf

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

File Description: application/xml

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

Periodic generalized functions

Authors: Szaz, A.

Source: Publicationes Mathematicae Debrecen. 25:229-235

Subject Terms: Differentiation Operators, Topological linear spaces of test functions, distributions and ultradistributions, Trigonometric Polynomials, Periodic Generalized Functions, 0101 mathematics, Fourier Coefficients, 01 natural sciences, Commutative Frechet Algebra, Operations with distributions and generalized functions

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Access URL: https://zbmath.org/3616959

Convolution of temperate distributions

Authors: Kučera, Jan

Source: Publicationes Mathematicae Debrecen. 33:323-327

Subject Terms: inductive and projective limits, Topological linear spaces of test functions, distributions and ultradistributions, space of convolution operators, temperate distributions, Sobolev derivatives, 0101 mathematics, 01 natural sciences, Operations with distributions and generalized functions

File Description: application/xml

Access URL: https://zbmath.org/4019766

Distributions of finite order in the operational calculus

Authors: Wysocki, Hubert

Source: Publicationes Mathematicae Debrecen. 38:49-68

Subject Terms: Leibniz formula, derivation, distributions of finite order, operational calculus, 0101 mathematics, 01 natural sciences, Operations with distributions and generalized functions

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Access URL: https://zbmath.org/9724

The neutrix distribution product $x^\lambda_+ \circ x^\mu_+$: The neutrix distribution product \(x_+^{\lambda}\circ x_+^{\mu}\)

Authors: Fisher, Brian, Kuribayashi, Yukio

Source: Publicationes Mathematicae Debrecen. 31:95-101

Subject Terms: neutrix limit, neutrix product, Operations with distributions and generalized functions

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Access URL: https://zbmath.org/3886564

A new algebra of distributions; initial-value problems involving Schwartz distributions. I: A new algebra of distributions; initial value problems involving Schwartz distributions. II

Authors: Krabbe, Gregers

Source: Publicationes Mathematicae Debrecen. 22:279-292

Subject Terms: Convolution as an integral transform, Topological linear spaces of test functions, distributions and ultradistributions, Linear ordinary differential equations and systems, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, 0101 mathematics, 01 natural sciences, Operations with distributions and generalized functions

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Access URL: https://zbmath.org/3570978
https://zbmath.org/3503938

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

File Description: application/xml

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

Der rechts- und linksseitige Wert einer Distribution im Punkte

Authors: Matusu, Josef

Source: Publicationes Mathematicae Debrecen. 25:89-95

Subject Terms: Point Limit of a Distribution, Load of a Beam, Rods (beams, columns, shafts, arches, rings, etc.), 0101 mathematics, 01 natural sciences, Integral of a Distribution, Operations with distributions and generalized functions

File Description: application/xml

Access URL: https://zbmath.org/3626056

On defining the distribution $\delta^{(r)}(f(x))$ for summable $f$: On defining the distribution \(\delta ^{(r)}(f(x))\) for summable f

Authors: Fisher, Brian

Source: Publicationes Mathematicae Debrecen. 32:233-241

Subject Terms: neutrix limit, distribution, 0101 mathematics, 01 natural sciences, Operations with distributions and generalized functions

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Access URL: https://zbmath.org/4013299

An algebraic approach to distributions on an open interval

Authors: Shultz, Harris S.

Source: Publicationes Mathematicae Debrecen. 20:73-77

Subject Terms: Topological linear spaces of test functions, distributions and ultradistributions, 0101 mathematics, 01 natural sciences, Operations with distributions and generalized functions

File Description: application/xml

Access URL: https://zbmath.org/3434527

Solving convolution equations in $S^{'}_+$ by numerical method: Solving convolution equations in \(S_ +'\) by numerical method

Authors: Pilipović, Stevan, Stojanovic, Mirjana

Source: Publicationes Mathematicae Debrecen. 40:17-33

Subject Terms: Convolution as an integral transform, Numerical analysis in abstract spaces, convolution equations, Laguerre series, Laguerre expansions, General harmonic expansions, frames, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), structural properties of the basic spaces, 0101 mathematics, 01 natural sciences, Operations with distributions and generalized functions

File Description: application/xml

Access URL: https://zbmath.org/56673
https://www.cris.uns.ac.rs/record.jsf?recordId=3255&source=OpenAIRE&language=en

On the product of distributions and the change of variable

Authors: Fisher, Brian

Source: Publicationes Mathematicae Debrecen. 35:37-42

Subject Terms: neutrix product, change of variable, 0101 mathematics, product of distributions, 01 natural sciences, Operations with distributions and generalized functions

File Description: application/xml

Access URL: https://zbmath.org/4094158

Hypoelliptic convolution equations in the space $\mathscr{H}'{M_p}$: Hypoelliptic convolution equations in the space \({\mathcal H}'\{M_ p\}\)

Authors: Pilipović, S., Takači, A.

Source: Publicationes Mathematicae Debrecen. 32:111-127

Subject Terms: Topological linear spaces of test functions, distributions and ultradistributions, Numerical computation of solutions to systems of equations, Fourier transform, 0101 mathematics, (p,q)-parametrix, 01 natural sciences, Operations with distributions and generalized functions

File Description: application/xml

Access URL: https://zbmath.org/3955725

On compositions of distributions

Authors: Kou, Huaizhong, Fisher, Brian

Source: Publicationes Mathematicae Debrecen. 40:279-290

Subject Terms: universal definition of the compositions of distributions, double neutrix limit, compositions of one-dimensional distributions, 0101 mathematics, 01 natural sciences, Operations with distributions and generalized functions

File Description: application/xml

Access URL: https://zbmath.org/40455

A theorem on the product of distributions

Authors: Fisher, B.

Source: Publicationes Mathematicae Debrecen. 27:243-249

Subject Terms: Dirac delta-function, regular sequence, 0101 mathematics, product of distributions, 01 natural sciences, Operations with distributions and generalized functions

File Description: application/xml

Access URL: https://zbmath.org/3709015

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

File Description: application/xml; application/pdf

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

On the convolution of distributions

Authors: Fisher, B.

Source: Publicationes Mathematicae Debrecen. 25:69-71

Subject Terms: Convolution as an integral transform, 0101 mathematics, 01 natural sciences, Operations with distributions and generalized functions

File Description: application/xml

Access URL: https://zbmath.org/3605428