Hacettepe Journal of Mathematics and Statistics, ISSN 1303-5010, 2016, Volume 45, Issue 6, pp. 1729 - 1742

We study polynomials in x and y of degree n + m : {Q(m,n) (x, y\t,q)}(n,m >= 0) that are related to the generalization of Poisson Mehler formula i.e. to the...

Poisson-Mehler summation formula. Orthogonal polynomials on the plane | Q-Hermite | Big q-Hermite | Orthogonal polynomials | Al-Salam Chihara | MATHEMATICS | big q-Hermite | Orthogonal polynomials on the plane | HERMITE | LIE | STATISTICS & PROBABILITY | q-Hermite | Al-Salam-Chihara | orthogonal polynomials | Poisson-Mehler summation formula

Poisson-Mehler summation formula. Orthogonal polynomials on the plane | Q-Hermite | Big q-Hermite | Orthogonal polynomials | Al-Salam Chihara | MATHEMATICS | big q-Hermite | Orthogonal polynomials on the plane | HERMITE | LIE | STATISTICS & PROBABILITY | q-Hermite | Al-Salam-Chihara | orthogonal polynomials | Poisson-Mehler summation formula

Journal Article

Applicable Analysis, ISSN 0003-6811, 03/2011, Volume 90, Issue 3-4, pp. 431 - 461

It is shown that the Whittaker-Kotel'nikov-Shannon sampling theorem of signal analysis, which plays the central role in this article, as well as (a particular...

Paley-Wiener's theorem | 30D10 | 46E22 | sampling theorem | Poisson's summation formula | bandlimited signals | functions of exponential type | reproducing kernel formula | 42C15 | 94A20 | Reproducing kernel formula | Functions of exponential type | Sampling theorem | Paley-wiener's theorem | Bandlimited signals | MATHEMATICS, APPLIED | Kernels | Theorems | Equivalence | Proving | Band theory | Fourier analysis | Sampling | Signal analysis | Interconnections

Paley-Wiener's theorem | 30D10 | 46E22 | sampling theorem | Poisson's summation formula | bandlimited signals | functions of exponential type | reproducing kernel formula | 42C15 | 94A20 | Reproducing kernel formula | Functions of exponential type | Sampling theorem | Paley-wiener's theorem | Bandlimited signals | MATHEMATICS, APPLIED | Kernels | Theorems | Equivalence | Proving | Band theory | Fourier analysis | Sampling | Signal analysis | Interconnections

Journal Article

Journal of Fourier Analysis and Applications, ISSN 1069-5869, 4/2017, Volume 23, Issue 2, pp. 442 - 461

The Poisson summation formula (PSF) describes the equivalence between the sampling of an analog signal and the periodization of its frequency spectrum. In...

Abstract Harmonic Analysis | Mathematical Methods in Physics | Polynomially growing functions | Fourier Analysis | Sampling theory | Tempered distributions | Signal,Image and Speech Processing | Approximations and Expansions | Mathematics | Poisson summation formula | Partial Differential Equations | Weighted Sobolev spaces | MATHEMATICS, APPLIED | BAND-LIMITED FUNCTIONS

Abstract Harmonic Analysis | Mathematical Methods in Physics | Polynomially growing functions | Fourier Analysis | Sampling theory | Tempered distributions | Signal,Image and Speech Processing | Approximations and Expansions | Mathematics | Poisson summation formula | Partial Differential Equations | Weighted Sobolev spaces | MATHEMATICS, APPLIED | BAND-LIMITED FUNCTIONS

Journal Article

Analysis and Mathematical Physics, ISSN 1664-2368, 12/2017, Volume 7, Issue 4, pp. 493 - 508

This paper presents the abstract notion of Poisson summation formulas for homogeneous spaces of compact groups. Let G be a compact group, H be a closed...

Inversion formula | Compact group | Primary 20G05 | Fourier transform | Mathematics | 43A85 | Poisson summation formula | 43A90 | Mathematical Methods in Physics | Secondary 43A30 | Analysis | Dual homogeneous space | Homogeneous space | Plancherel (trace) formula | MATHEMATICS | MATHEMATICS, APPLIED | RELATIVE CONVOLUTIONS | FOURIER-ANALYSIS

Inversion formula | Compact group | Primary 20G05 | Fourier transform | Mathematics | 43A85 | Poisson summation formula | 43A90 | Mathematical Methods in Physics | Secondary 43A30 | Analysis | Dual homogeneous space | Homogeneous space | Plancherel (trace) formula | MATHEMATICS | MATHEMATICS, APPLIED | RELATIVE CONVOLUTIONS | FOURIER-ANALYSIS

Journal Article

Results in Mathematics, ISSN 1422-6383, 5/2011, Volume 59, Issue 3, pp. 359 - 400

This paper is concerned with the two summation formulae of Euler–Maclaurin (EMSF) and Abel–Plana (APSF) of numerical analysis, that of Poisson (PSF) of Fourier...

Quadrature formulae | Abel–Plana summation formula | 65B15 | 65D32 | Approximate sampling formula | Mathematics, general | Mathematics | Euler–Maclaurin summation formula | Poisson summation formula | Whittaker–Kotel’nikov–Shannon sampling theorem | 94A20 | Bandlimited signals | Abel-Plana summation formula | Euler-Maclaurin summation formula | Whittaker-Kotel'nikov-Shannon sampling theorem | MATHEMATICS | MATHEMATICS, APPLIED | EXPONENTIAL-TYPE | THEOREM | ERROR

Quadrature formulae | Abel–Plana summation formula | 65B15 | 65D32 | Approximate sampling formula | Mathematics, general | Mathematics | Euler–Maclaurin summation formula | Poisson summation formula | Whittaker–Kotel’nikov–Shannon sampling theorem | 94A20 | Bandlimited signals | Abel-Plana summation formula | Euler-Maclaurin summation formula | Whittaker-Kotel'nikov-Shannon sampling theorem | MATHEMATICS | MATHEMATICS, APPLIED | EXPONENTIAL-TYPE | THEOREM | ERROR

Journal Article

6.
Full Text
New summation and transformation formulas of the Poisson, Müntz, Möbius and Voronoi type

Integral Transforms and Special Functions, ISSN 1065-2469, 10/2015, Volume 26, Issue 10, pp. 768 - 795

Starting from the classical summation formulas and basing on properties of the Mellin transform and Ramanujan's identities, which represent a ratio of products...

Riemann's hypothesis | Müntz operator | 33C10 | 11N 37 | Fourier transform | Poisson summation formula | Voronoi summation formula | Möbius transform | arithmetic functions | 44A15 | Ramanujan's identities | 11M36 | 11M06 | Riemann's zeta function | Müntz formula | Mellin transform | MATHEMATICS, APPLIED | MATHEMATICS | Mobius transform | Muntz formula | INDEX TRANSFORMS | Muntz operator

Riemann's hypothesis | Müntz operator | 33C10 | 11N 37 | Fourier transform | Poisson summation formula | Voronoi summation formula | Möbius transform | arithmetic functions | 44A15 | Ramanujan's identities | 11M36 | 11M06 | Riemann's zeta function | Müntz formula | Mellin transform | MATHEMATICS, APPLIED | MATHEMATICS | Mobius transform | Muntz formula | INDEX TRANSFORMS | Muntz operator

Journal Article

Mathematical Problems in Engineering, ISSN 1024-123X, 2017, Volume 2017, pp. 1 - 5

This paper investigates the generalized pattern of Poisson summation formulae from the special affine Fourier transform (SAFT) and offset Hilbert transform...

DOMAIN | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | CONVOLUTION THEOREM | FRACTIONAL FOURIER | SIGNALS | LINEAR CANONICAL TRANSFORM | EIGENFUNCTIONS | Poisson's equation | Fourier transformations | Research | Mathematical research | Mappings (Mathematics) | Studies | Fourier transforms | Applied mathematics | Digital signal processors | Signal processing | Laplace transforms | Hilbert transformation

DOMAIN | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | CONVOLUTION THEOREM | FRACTIONAL FOURIER | SIGNALS | LINEAR CANONICAL TRANSFORM | EIGENFUNCTIONS | Poisson's equation | Fourier transformations | Research | Mathematical research | Mappings (Mathematics) | Studies | Fourier transforms | Applied mathematics | Digital signal processors | Signal processing | Laplace transforms | Hilbert transformation

Journal Article

Forum Mathematicum, ISSN 0933-7741, 05/2017, Volume 29, Issue 3, pp. 501 - 517

We investigate convolution semigroups of probability measures with continuous densities on locally compact abelian groups, which have a discrete subgroup such...

60B15 | adèles | Fourier transform | 11F85 | Gel’fand–Graev gamma function | Locally compact abelian group | Poisson summation formula | semistable | 43A25 | idèles | convolution semigroup | 11R56 | Riemann–Roch theorem, Bruhat–Schwartz space | 60E07 | discrete subgroup | Riemann-roch theorem | Semistable | AdèLes | p-adic number | Poisson summation Formula | Convolution semigroup | α-stable | Bruhat-schwartz space | Gel'fand-graev gamma function | Discrete subgroup | MATHEMATICS, APPLIED | NUMBERS | P-ADICS | Gel'fand-Graev gamma function | ideles | adeles | MATHEMATICS | Bruhat-Schwartz space | alpha-stable | Riemann-Roch theorem

60B15 | adèles | Fourier transform | 11F85 | Gel’fand–Graev gamma function | Locally compact abelian group | Poisson summation formula | semistable | 43A25 | idèles | convolution semigroup | 11R56 | Riemann–Roch theorem, Bruhat–Schwartz space | 60E07 | discrete subgroup | Riemann-roch theorem | Semistable | AdèLes | p-adic number | Poisson summation Formula | Convolution semigroup | α-stable | Bruhat-schwartz space | Gel'fand-graev gamma function | Discrete subgroup | MATHEMATICS, APPLIED | NUMBERS | P-ADICS | Gel'fand-Graev gamma function | ideles | adeles | MATHEMATICS | Bruhat-Schwartz space | alpha-stable | Riemann-Roch theorem

Journal Article

Journal of Number Theory, ISSN 0022-314X, 2010, Volume 130, Issue 3, pp. 738 - 766

In this paper, the convergence of the Euler product of the Hecke zeta-function ζ ( s , χ ) is proved on the line R ( s ) = 1 with s ≠ 1 . A certain functional...

Poisson's summation formula | Hankel transformation | MATHEMATICS

Poisson's summation formula | Hankel transformation | MATHEMATICS

Journal Article

10.
Full Text
A Generalized Poisson Summation Formula and its Application to Fast Linear Convolution

IEEE Signal Processing Letters, ISSN 1070-9908, 09/2011, Volume 18, Issue 9, pp. 501 - 504

In this letter, a generalized Fourier transform is introduced and its corresponding generalized Poisson summation formula is derived. For discrete, Fourier...

Convolution | Discrete Fourier transforms | Digital signal processing | Complexity theory | Approximation methods | linear filtering | Generalized Poisson summation formula | Frequency domain analysis | weighted circular convolution | ENGINEERING, ELECTRICAL & ELECTRONIC

Convolution | Discrete Fourier transforms | Digital signal processing | Complexity theory | Approximation methods | linear filtering | Generalized Poisson summation formula | Frequency domain analysis | weighted circular convolution | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Computational Methods and Function Theory, ISSN 1617-9447, 12/2016, Volume 16, Issue 4, pp. 689 - 697

Journal Article

Computational Methods and Function Theory, ISSN 1617-9447, 12/2016, Volume 16, Issue 4, pp. 689 - 697

The Poisson summation formula for Hardy spaces $$H^p\left( T_\Gamma \right) $$ H p T Γ in tubes $$T_\Gamma \subset \mathbb {C}^n$$ T Γ ⊂ C n for $$p\in \left(...

Computational Mathematics and Numerical Analysis | Tube area | Open cone | Functions of a Complex Variable | 42B30 | Analysis | Absolute and locally-uniform convergence | 42B08 | Mathematics | Poisson summation formula | 42B05 | Hardy space

Computational Mathematics and Numerical Analysis | Tube area | Open cone | Functions of a Complex Variable | 42B30 | Analysis | Absolute and locally-uniform convergence | 42B08 | Mathematics | Poisson summation formula | 42B05 | Hardy space

Journal Article

Communications on Pure and Applied Analysis, ISSN 1534-0392, 01/2013, Volume 12, Issue 1, pp. 359 - 373

We show that using spectral theory of a finite family of pair-wise commuting Laplace operators and the spectral properties of the periodic Laplace operator...

Eigenvalue | Poisson summation formula | Eigenfunction | Joint spectral resolution | Commuting Laplace operators | MATHEMATICS | MATHEMATICS, APPLIED | eigenfunction | joint spectral resolution | eigenvalue

Eigenvalue | Poisson summation formula | Eigenfunction | Joint spectral resolution | Commuting Laplace operators | MATHEMATICS | MATHEMATICS, APPLIED | eigenfunction | joint spectral resolution | eigenvalue

Journal Article

Bulletin of Mathematical Sciences, ISSN 1664-3607, 12/2014, Volume 4, Issue 3, pp. 481 - 525

The present paper deals mainly with seven fundamental theorems of mathematical analysis, numerical analysis, and number theory, namely the generalized Parseval...

Reproducing kernel formula | 30D10 | Parseval formula | Poisson’s summation formula | 41A80 | 30D05 | Mathematics | Euler–Maclaurin summation formula | Riemann’s zeta function | Bandlimited and non-bandlimited functions | Mathematics, general | Sampling theorem | 42A38 | 94A20 | Poisson's summation formula | RECONSTRUCTION | SUMMATION FORMULA | EULER-MACLAURIN | MATHEMATICS | Euler-Maclaurin summation formula | Riemann's zeta function | DIRICHLET SERIES | RIEMANNS FUNCTIONAL-EQUATION

Reproducing kernel formula | 30D10 | Parseval formula | Poisson’s summation formula | 41A80 | 30D05 | Mathematics | Euler–Maclaurin summation formula | Riemann’s zeta function | Bandlimited and non-bandlimited functions | Mathematics, general | Sampling theorem | 42A38 | 94A20 | Poisson's summation formula | RECONSTRUCTION | SUMMATION FORMULA | EULER-MACLAURIN | MATHEMATICS | Euler-Maclaurin summation formula | Riemann's zeta function | DIRICHLET SERIES | RIEMANNS FUNCTIONAL-EQUATION

Journal Article

Journal of Number Theory, ISSN 0022-314X, 10/2018, Volume 191, pp. 258 - 272

Let λi(n), i=1,2,3, denote the normalized Fourier coefficients of a holomorphic eigenform or Maass cusp form. In this paper we shall consider the...

Maass forms | Voronoi summation formula | Poisson summation formula | Hecke eigenforms | FORMS | MATHEMATICS

Maass forms | Voronoi summation formula | Poisson summation formula | Hecke eigenforms | FORMS | MATHEMATICS

Journal Article

Applied Mathematics, ISSN 1005-1031, 09/2014, Volume 29, Issue 3, pp. 329 - 338

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 10/2019, Volume 50, Issue 1, pp. 45 - 60

Suppose that q and r are two distinct large primes. Let g be a cuspidal Hecke eigenform of level 1 and even weight $$k_1$$ k 1 and $$H_{k_2}(q)$$ H k 2 ( q )...

Petersson formula | Functions of a Complex Variable | Twisted L -functions | Field Theory and Polynomials | Mathematics | 11F30 | Voronoi summation formula | Poisson summation formula | Stationary phase method | 11F11 | Fourier Analysis | 11L05 | Number Theory | Combinatorics | MATHEMATICS | MOMENT | BOUNDS | Twisted L-functions | HEEGNER POINTS | Energy conservation | Aquatic resources

Petersson formula | Functions of a Complex Variable | Twisted L -functions | Field Theory and Polynomials | Mathematics | 11F30 | Voronoi summation formula | Poisson summation formula | Stationary phase method | 11F11 | Fourier Analysis | 11L05 | Number Theory | Combinatorics | MATHEMATICS | MOMENT | BOUNDS | Twisted L-functions | HEEGNER POINTS | Energy conservation | Aquatic resources

Journal Article

Calcolo, ISSN 0008-0624, 9/2018, Volume 55, Issue 3, pp. 1 - 33

The general Poisson summation formula of Mellin analysis can be considered as a quadrature formula for the positive real axis with remainder. For Mellin...

Quadrature formulae | 65D30 | Mellin transforms | Numerical Analysis | 65D32 | 26A33 | 41A80 | Mathematics | Theory of Computation | Polar-analytic functions | Mellin–Poisson summation formulae | MATHEMATICS | MATHEMATICS, APPLIED | Mellin-Poisson summation formulae | PALEY-WIENER THEOREM | RULES | Error analysis | Convergence

Quadrature formulae | 65D30 | Mellin transforms | Numerical Analysis | 65D32 | 26A33 | 41A80 | Mathematics | Theory of Computation | Polar-analytic functions | Mellin–Poisson summation formulae | MATHEMATICS | MATHEMATICS, APPLIED | Mellin-Poisson summation formulae | PALEY-WIENER THEOREM | RULES | Error analysis | Convergence

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 04/2007, Volume 57, Issue 5, pp. 1331 - 1343

Diffraction images with continuous rotation symmetry arise from amorphous systems, but also from regular crystals when investigated by powder diffraction. On...

Powder diffraction | Poisson's summation formula | Pinwheel patterns | Circular symmetry | MATHEMATICS, APPLIED | pinwheel patterns | SYMMETRY | TILINGS | circular symmetry | PHYSICS, MATHEMATICAL | EQUIVALENCE | powder diffraction

Powder diffraction | Poisson's summation formula | Pinwheel patterns | Circular symmetry | MATHEMATICS, APPLIED | pinwheel patterns | SYMMETRY | TILINGS | circular symmetry | PHYSICS, MATHEMATICAL | EQUIVALENCE | powder diffraction

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 03/2017, Volume 50, Issue 15

Journal Article

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