Positivity properties in noncommutative convolution algebras with applications in pseudo-differential calculus

DOI10.1016/S0007-4497(02)00003-9zbMath1031.47024MaRDI QIDQ1395894

Joachim Toft

Publication date: 1 July 2003

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

zbMATH Keywords

pseudodifferential operatorstwisted convolutionSchatten-classes

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Positive linear operators and order-bounded operators (47B65) Positive definite functions on groups, semigroups, etc. (43A35) Singularity in context of PDEs (35A21) Pseudodifferential operators (47G30) Wave front sets in context of PDEs (35A18)

Related Items (8)

Fourier modulation spaces and positivity in twisted convolution algebra ⋮ Multiplication properties in pseudo-differential calculus with small regularity on the symbols ⋮ Strong ultra-regularity properties for positive elements in the twisted convolutions ⋮ Abstract composition laws and their modulation spaces ⋮ The wave front set of the Wigner distribution and instantaneous frequency ⋮ Weyl product algebras and modulation spaces ⋮ Multiplication Properties in Gelfand–Shilov Pseudo-differential Calculus ⋮ Boundedness of Gevrey and Gelfand-Shilov kernels of positive semi-definite operators

Cites Work

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• Continuity properties in non-commutative convolution algebras, with applications in pseudo-differential calculus
• An algebra of pseudodifferential operators and quantum mechanics in phase space
• Harmonic Analysis in Phase Space. (AM-122)
• The weyl calculus of pseudo-differential operators
• On positivity of pseudo-differential operators
• Regularizations, decompositions and lower bound problems in the weyl calculus
• Lower bounds for pseudo-differential operators
• Subalgebras to a Wiener type algebra of pseudo-differential operators

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