A convolution operator related to the generalized Mehler-Fock and Kontorovich-Lebedev transforms

DOI10.1007/s00025-011-0214-xzbMath1267.44002OpenAlexW1982143577MaRDI QIDQ1936942

Nelson Vieira, Semyon B. Yakubovich, M. Manuela Rodrigues

Publication date: 8 February 2013

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-011-0214-x

zbMATH Keywords

convolution integral equationsKontorovich-Lebedev transformmodified Bessel functionassociated Legendre functionsindex integralsgeneralized Mehler-Fock transform

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Linear integral equations (45A05) General integral transforms (44A05)

Related Items (7)

Product of pseudo-differential operators associated with zero order Mehler-Fock transform ⋮ Composition and commutator of pseudo-differential operators in the framework of zero-order Mehler-Fock transform domain ⋮ The convolution for zero-order Mehler–Fock transform and pseudo-differential operator ⋮ Some connections between the spherical and parabolic bases on the cone expressed in terms of the Macdonald function ⋮ A Dirac delta-type orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices ⋮ Certain connections between the spherical and hyperbolic bases on the cone and formulas for related special functions ⋮ Zero-order Mehler-Fock transform and Sobolev-type space

Cites Work

• An index integral and convolution operator related to the kontorovich-lebedev and mehler-Fock transforms
• On the least values of \(L_{p}\)-norms for the Kontorovich--Lebedev transform and its convolution
• The Mehler-Fock transform of general order and arbitrary index and its inversion
• Index integral representations for connection between cartesian, cylindrical, and spheroidal systems
• On the Mehler‐Fock Transform in L_p‐Space
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