The construction of Dirichlet and de la Vallée-Poussin–Nikol’skiĭ kernels for $\mathrm {j}$-Bessel Fourier integrals

DOI10.1090/mosc/242zbMath1332.33007OpenAlexW2202695724MaRDI QIDQ2788920

Lev N. Lyakhov

Publication date: 23 February 2016

Published in: Transactions of the Moscow Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/mosc/242

zbMATH Keywords

Dirichlet kernelBessel functionFourier-Bessel transformgeneralized shiftde la Vallée-Poussin kerneleven and odd Bessel \(\mathrm{j}\)-functionsHankel (Bessel) transform

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (9)

Interpolation formulas for B-derivative of the Schlömilch \(j\)-polynomial ⋮ Inversion formulas for integral operations of weighted plane wave type ⋮ Spherical transformation of generalized Poisson shift and properties of weighted Lebesgue classes of functions ⋮ Uniqueness of the solution of the Dirichlet problem for the Poisson equation with a singular \(\Delta_B\)-Kipriyanov operator ⋮ On the fundamental solution of a \(D_B \)-hyperbolic operator with a Bessel operator in time ⋮ Huygens principle for singular hyperbolic equations ⋮ Differential and integral operations in hidden spherical symmetry and the dimension of the Koch curve ⋮ Kipriyanov-Beltrami operator with negative dimension of the Bessel operators and the singular Dirichlet problem for the \(B \)-harmonic equation ⋮ Norms of the positive powers of the Bessel operator in the spaces of even Schlömilch j-polynomials

Cites Work

• On a Kipriyanov problem for a singular ultrahyperbolic equation
• Full Fourier-Bessel transform and the algebra of singular pseudodifferential operators
• Schlömilch polynomials: Riesz's interpolation formula for B-derivatives and Bernstein's inequality for Weyl-Marchaud fractional B-derivatives
• Singular integrals generated by a general translation operator. II
• ON A CLASS OF ONE-DIMENSIONAL SINGULAR PSEUDODIFFERENTIAL OPERATORS
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