Characterization of Fourier hyperfunctions by solutions of the Hermite heat equation

DOI10.1080/10652460701320729zbMath1138.46031OpenAlexW2131474470MaRDI QIDQ5422406

Dohan Kim, Soon-Yeong Chung, Bishnu Prasad Dhungana

Publication date: 19 October 2007

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652460701320729

zbMATH Keywords

Hermite functionsFourier hyperfunctionsHermite heat equationMehler kernel

Mathematics Subject Classification ID

Heat equation (35K05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Hyperfunctions, analytic functionals (46F15) Initial value problems for second-order parabolic equations (35K15) Topological linear spaces of test functions, distributions and ultradistributions (46F05)

Related Items (5)

Mehler kernel approach to Fourier ultra-hyperfunctions ⋮ A characterization of the tempered distributions with regular closed support by Bloch equations ⋮ An existence result of the Cauchy Dirichlet problem for the Hermite heat equation ⋮ A characterization of distributions of exponential growth with support in a regular closed set ⋮ Uniqueness in the Cauchy problem for the Hermite heat equation

Cites Work

• An example of nonuniqueness of the Cauchy problem for the Hermite heat equation
• Mehler kernel approach to tempered distributions
• Uniqueness in the Cauchy problem for the heat equation
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