Asymptotic expansions of solutions to the heat equations with initial value in the dual of Gelfand-Shilov spaces

DOI10.3836/TJM/1327931402zbMath1242.46050OpenAlexW2051422740MaRDI QIDQ410138

Yasuyuki Oka

Publication date: 3 April 2012

Published in: Tokyo Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3836/tjm/1327931402

zbMATH Keywords

heat equationasymptotic expansionBorel summabilityWeyl transformGel'fand-Shilov space

Mathematics Subject Classification ID

Heat equation (35K05) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Hyperfunctions, analytic functionals (46F15) Initial value problems for second-order parabolic equations (35K15) Topological linear spaces of test functions, distributions and ultradistributions (46F05)

Cites Work

• Spaces of test functions via the STFT
• A calculus approach to hyperfunctions III
• On the Weyl Transform with Symbol in the Gel'fand-Shilov Space and its Dual Space
• ASYMPTOTIC EXPANSIONS OF THE SOLUTIONS TO THE HEAT EQUATIONS WITH HYPERFUNCTIONS INITIAL VALUE
• An improvement of Watson’s theorem on Borel summability
• Characterizations of the Gelfand-Shilov spaces via Fourier transforms
• Mathematical Aspects of the Weyl Correspondence
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