The fundamental solution for a degenerate parabolic pseudo-dierential operator

DOI10.3792/pja/1195519102zbMath0303.35073OpenAlexW2080164258MaRDI QIDQ4059319

Chisato Tsutsumi

Publication date: 1974

Published in: Proceedings of the Japan Academy, Series A, Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pja/1195519102

Mathematics Subject Classification ID

Initial value problems for higher-order parabolic equations (35K30) Initial value problems for PDEs with pseudodifferential operators (35S10)

Related Items (13)

Parametrix construction of the transition probability density of the solution to an SDE driven by \(\alpha\)-stable noise ⋮ Fundamental solution for super-critical non-symmetric Lévy-type operators ⋮ Cauchy problem for a class of pseudodifferential systems with smooth symbols ⋮ On symbols of fundamental solutions of parabolic systems ⋮ Optimal regularity of a degenerate elliptic equation ⋮ On weak uniqueness and distributional properties of a solution to an SDE with \(\alpha\)-stable noise ⋮ The fundamental solution for a parabolic pseudo-differential operator and parametrices for degenerate operators ⋮ On the fundamental solution of a degenerate parabolic system ⋮ Heat kernels of non-symmetric Lévy-type operators ⋮ Factorizations and fundamental solutions for differential operators of elliptic-hyperbolic type ⋮ Pseudodifferential Multi-Product Representation of the Solution Operator of a Parabolic Equation ⋮ Phase space Feynman path integrals of higher order parabolic type with general functional as integrand ⋮ Construction and heat kernel estimates of generalstable-like Markov processes

Cites Work

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• Pseudo-differential operators of multiple symbol and the Calderon- Vaillancourt theorem
• Complex powers of hypoelliptic pseudo-differential operators with applications
• Hypoellipticité des équations paraboliques
• On some degenerate parabolic equations II
• Oscillatory integrals of symbols of pseudo-differential operators on $R^n $ and operators of Fredholm type
• $L^p$-theory of pseudo-differential operators

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