An index integral and convolution operator related to the kontorovich-lebedev and mehler-Fock transforms

DOI10.1007/s11785-010-0112-3zbMath1274.44007OpenAlexW2033029611MaRDI QIDQ371725

Semyon B. Yakubovich

Publication date: 10 October 2013

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-010-0112-3

zbMATH Keywords

convolution integral equationsKontorovich-Lebedev transformMehler-Fock transformmodified Bessel functionassociated Legendre functionsParseval equalityindex integrals

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Linear integral equations (45A05) General integral transforms (44A05)

Related Items (6)

Product of pseudo-differential operators associated with zero order Mehler-Fock transform ⋮ A convolution operator related to the generalized Mehler-Fock and Kontorovich-Lebedev transforms ⋮ The integro‐differential operators of infinite order on the half line related to the Legendre operator ⋮ The convolution for zero-order Mehler–Fock transform and pseudo-differential operator ⋮ A Dirac delta-type orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices ⋮ Heat kernel in the framework of zero order Mehler-Fock transform

Cites Work

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• On the least values of \(L_{p}\)-norms for the Kontorovich--Lebedev transform and its convolution

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