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  • Produktbild: Parabolicity, Volterra Calculus, and Conical Singularities
  • Produktbild: Parabolicity, Volterra Calculus, and Conical Singularities

Parabolicity, Volterra Calculus, and Conical Singularities A Volume of Advances in Partial Differential Equations

Aus der Reihe Operator Theory: Advances and Applications

Fr. 73.90

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

13.10.2012

Herausgeber

Sergio Albeverio + weitere

Verlag

Springer Basel

Seitenzahl

359

Maße (L/B/H)

23.5/15.5/2.1 cm

Gewicht

575 g

Auflage

Softcover reprint of the original 1st ed. 2002

Sprache

Englisch

ISBN

978-3-0348-9469-2

Beschreibung

Portrait

Dipl.-Kaufmann Michael Demuth ist Geschäftsführer der Vermögensberatungsgesellschaft Creative Capital GmbH.
Bert-Wolfgang Schulze ist emeritierter Professor am Institut für Mathematik an der Universität Potsdam, Deutschland. Vor der politischen Wende war er Professor am Karl-Weierstrass-Institut in Berlin, 1984 Euler-Medaille der Akademie der Wisenschaften in Berlin. 1992-96 war er Leiter der Max-Planck-Arbeitsgruppe 'Partielle Differentialgleichungen und Komplexe Analysis' in Potsdam. Nach anfänglichem Studium in Geophysik erhielt er sein Universitätsdiplom in Mathematik in Leipzig 1968. Die Promotion zum Dr. rer.nat. 1970 und die Habilitation in Mathematik 1974 erfolgten an der Universität Rostock. Seine wissenschaftlichen Aktivitäten umfassen Potentialtheorie, Randwert-Probleme, pseudo-differentielle Algebren und Index-Theorie auf berandeten Mannigfaltgikeiten und Räumen mit Singularitäten, darunterTransmissions- und Riss Probleme, Asymptotik von Lösungen, Randwert-Theorie mit globalen Projektionsbedingungen.

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

13.10.2012

Herausgeber

Verlag

Springer Basel

Seitenzahl

359

Maße (L/B/H)

23.5/15.5/2.1 cm

Gewicht

575 g

Auflage

Softcover reprint of the original 1st ed. 2002

Sprache

Englisch

ISBN

978-3-0348-9469-2

Herstelleradresse

Springer-Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE

Email: GPSR Kontakt

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  • Produktbild: Parabolicity, Volterra Calculus, and Conical Singularities
  • Produktbild: Parabolicity, Volterra Calculus, and Conical Singularities
  • Volterra Families of Pseudodifferential Operators.- 1. Basic notation and general conventions.- 1.1. Sets of real and complex numbers.- 1.2. Multi-index notation.- 1.3. Functional analysis and basic function spaces.- 1.4. Tempered distributions and the Fourier transform.- 2. General parameter-dependent symbols.- 2.1. Asymptotic expansion.- 2.2. Homogeneity and classical symbols.- 3. Parameter-dependent Volterra symbols.- 3.1. Kernel cut-off and asymptotic expansion.- 3.2. The translation operator in Volterra symbols.- 4. The calculus of pseudodifferential operators.- 4.1. Elements of the calculus.- 4.2. The formal adjoint operator.- 4.3. Sobolev spaces and continuity.- 4.4. Coordinate invariance.- 5. Ellipticity and parabolicity.- 5.1. Ellipticity in the general calculus.- 5.2. Parabolicity in the Volterra calculus.- References.- The Calculus of Volterra Mellin Pseudodifferential Operators with Operator-valued Symbols.- 1. Preliminaries on function spaces and the Mellin transform.- 1.1. A Paley-Wiener type theorem.- 1.2. The Mellin transform in distributions.- 2. The calculus of Volterra symbols.- 2.1. General anisotropic and Volterra symbols.- 2.1.1. Hilbert spaces with group-actions.- 2.1.2. Definition of the symbol spaces.- 2.1.3. Asymptotic expansion.- 2.1.4. The translation operator in Volterra symbols.- 2.2. Holomorphic Volterra symbols.- 3. The calculus of Volterra Mellin operators.- 3.1. General Volterra Mellin operators.- 3.2. Continuity in Mellin Sobolev spaces.- 3.3. Volterra Mellin operators with analytic symbols.- 4. Kernel cut-off and Mellin quantization.- 4.1. The Mellin kernel cut-off operator.- 4.2. Degenerate symbols and Mellin quantization.- 5. Parabolicity and Volterra parametrices.- 5.1. Ellipticity and parabolicity on symbolic level.- 5.2. The parametrix construction.- References.- On the Inverse of Parabolic Systems of Partial Differential Equations of General Form in an Infinite Space-Time Cylinder.- 1. Preliminary material.- 1.1. Basic notation and general conventions.- Functional analysis and basic function spaces.- Preliminaries on function spaces and the Mellin transform.- Global analysis.- 1.2. Finitely meromorphic Fredholm families in ?-algebras.- 1.3. Volterra integral operators.- Some notes on abstract kernels.- 2. Abstract Volterra pseudodifferential calculus.- 2.1. Anisotropic parameter-dependent symbols.- Asymptotic expansion.- Classical symbols.- 2.2. Anisotropic parameter-dependent operators.- Elements of the calculus.- Ellipticity and parametrices.- Sobolev spaces and continuity.- Coordinate invariance.- 2.3. Parameter-dependent Volterra symbols.- Kernel cut-off and asymptotic expansion of Volterra symbols.- The translation operator in Volterra symbols.- 2.4. Parameter-dependent Volterra operators.- Elements of the calculus.- Continuity and coordinate invariance.- Parabolicity for Volterra pseudodifferential operators.- 2.5. Volterra Mellin calculus.- Continuity in Mellin Sobolev spaces.- 2.6. Analytic Volterra Mellin calculus.- Elements of the calculus.- The Mellin kernel cut-off operator and asymptotic expansion.- Degenerate symbols and Mellin quantization.- 2.7. Volterra Fourier operators with global weight conditions.- 3. Parameter-dependent Volterra calculus on a closed manifold.- 3.1. Anisotropic parameter-dependent operators.- Ellipticity and parametrices.- 3.2. Parameter-dependent Volterra operators.- Kernel cut-off behaviour and asymptotic expansion.- The translation operator in Volterra pseudodifferential operators.- Parabolicity for Volterra operators on manifolds.- 4. Weighted Sobolev spaces.- 4.1. Anisotropic Sobolev spaces on the infinite cylinder.- 4.2. Anisotropic Mellin Sobolev spaces.- Mellin Sobolev spaces with asymptotics.- 4.3. Cone Sobolev spaces.- 5. Calculi built upon parameter-dependent operators.- 5.1. Anisotropic meromorphic Mellin symbols.- 5.2. Meromorphic Volterra Mellin symbols.- Mellin quantization.- 5.3. Elements of the Mellin calculus.- Ellipticity and Parabolicity.- 5.4. Elements of the Fourier calculus with global weights.- Ellipticity and Parabolicity.- 6. Volterra cone calculus.- 6.1. Green operators.- 6.2. The algebra of conormal operators.- Operators that generate asymptotics.- Calculus of conormal symbols.- The operator calculus.- Smoothing Mellin and Green operators.- 6.3. The algebra of Volterra cone operators.- The symbolic structure.- Compositions and adjoints.- 6.4. Ellipticity and Parabolicity.- Parabolic reductions of orders.- 7. Remarks on the classical theory of parabolic PDE.- References.- On the Factorization of Meromorphic Mellin Symbols.- 1. Introduction.- 2. Preliminaries.- 2.1. Parameter-dependent operators.- 2.2. Meromorphic Mellin symbols.- 2.3. Reduction to holomorphic Mellin symbols.- 3. Logarithms of pseudodifferential operators.- 3.1. The classes L? log (X; ?).- 3.2. The exponential map.- 3.3. The topological invariant ?(A).- 3.4. Characterization of the image of exp.- 4. The kernel cut-off technique.- 5. Proof of the main theorem.- 5.1. Beginning of the proof.- 5.2. Continuation of the proof.- 5.3. The remaining case for dim X = 1.- References.- Coordinate Invariance of the Cone Algebra with Asymptotics.- 1. Cone operators on the half-axis.- 1.1. The cone algebra.- 1.2. Spaces with asymptotics and Green operators.- 1.3. Push-forward of Mellin operators.- 1.4. Invariance of the cone algebra.- Appendix to Sect. 1.4: An intrinsic interpretation of the principal symbol.- 1.5. Symbolic rules.- 2. Operators on higher-dimensional cones.- 2.1. The cone algebra.- 2.2. Spaces with asymptotics and Green operators.- 2.3. Push-forward of Mellin operators.- 2.4. Invariance of the cone algebra.- References.