An embedding theorem of Sobolev type for an operator with singularity

DOI10.1090/S0002-9939-97-03642-3zbMath0870.46020OpenAlexW1852167654MaRDI QIDQ4333020

Shuji Watanabe

Publication date: 19 February 1997

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-97-03642-3

zbMATH Keywords

Fourier transformCauchy problemsone-dimensional harmonic oscillatorEmbedding theorem of Sobolev typeoperator with singularitypartial differential equations with singular coefficientsWigner's commutation relation

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) One-parameter semigroups and linear evolution equations (47D06) Linear symmetric and selfadjoint operators (unbounded) (47B25) Initial value problems for linear higher-order PDEs (35G10)

Related Items (4)

THE EXPLICIT SOLUTIONS TO THE TIME-DEPENDENT SCHRÖDINGER EQUATIONS WITH THE SINGULAR POTENTIALS AND ⋮ The explicit solution of a diffusion equation with singularity ⋮ Hardy inequalities for functions vanishing at negligible sets and its applications ⋮ Quantum Mechanics on S 1 Based on Dirac Formalism

Cites Work

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• On the perturbation of linear operators in Banach and Hilbert spaces
• Über die Selbstadjungiertheit von Schrödinger-Operatoren
• Self-Adjointness of the Momentum Operator with a Singular Term
• Self-adjointness of the operators in Wigner’s commutation relations
• Sobolev type theorems for an operator with singularity
• Do the Equations of Motion Determine the Quantum Mechanical Commutation Relations?
• A Note on the Quantum Rule of the Harmonic Oscillator

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