The heat kernel and Heisenberg inequalities related to the Kontorovich-Lebedev transform

DOI10.3934/cpaa.2011.10.745zbMath1235.44006OpenAlexW2325353973MaRDI QIDQ651997

Semyon B. Yakubovich

Publication date: 19 December 2011

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2011.10.745

zbMATH Keywords

Mellin transformconvolutiondiffusion equationuncertainty principleheat kernelKontorovich-Lebedev transformmodified Bessel functionHeisenberg inequalityPlancherel theory

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Heat equation (35K05) Transform methods (e.g., integral transforms) applied to PDEs (35A22)

Related Items (9)

The convolution for the Kontorovich-Lebedev transform revisited ⋮ Uncertainty principles for the continuous Kontorovich Lebedev wavelet transform ⋮ The spectral expansion approach to index transforms and connections with the theory of diffusion processes ⋮ Markov processes related to the stationary measure for the open KPZ equation ⋮ Tikhonov regularisation for the Weierstrass transform associated with the Kontorovich–Lebedev transform ⋮ The use of the Kontorovich–Lebedev transform in an analysis of regularized Schrödinger equation ⋮ Summability experiments with a class of divergent inverse Kontorovich-Lebedev transforms ⋮ Heat kernel in the framework of zero order Mehler-Fock transform ⋮ On the Yor integral and a system of polynomials related to the Kontorovich–Lebedev transform

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