
Pseudo-Differential Operators, Generalized Functions and Asymptotics
Birkhäuser (Publisher)
Published on 6. March 2013
Book
Hardback
VIII, 370 pages
978-3-0348-0584-1 (ISBN)
Description
This volume consists of twenty peer-reviewed papers from the special session on pseudodifferential operators and the special session on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples' Friendship University of Russia in Moscow on August 22-27, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifolds with edges, heat kernels and Green functions of sub-Laplacians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, Lp-boundedness of pseudo-differential operators on the torus, and pseudo-differential operators related to time-frequency analysis. The second group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlinear differential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differential equations. This second group of papers are related to the third collection of papers via the setting of Colombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volume contains the synergies of the three areas treated and is a useful complement to volumes 155, 164, 172, 189, 205 and 213 published in the same series in, respectively, 2004, 2006, 2007, 2009, 2010 and 2011.
More details
Series
Edition
2013 ed.
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
5 s/w Abbildungen, 1 farbige Abbildung
VIII, 370 p. 6 illus., 1 illus. in color.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 25 mm
Weight
735 gr
ISBN-13
978-3-0348-0584-1 (9783034805841)
DOI
10.1007/978-3-0348-0585-8
Schweitzer Classification
Other editions
Additional editions

Shahla Molahajloo | Stevan Pilipovic | Joachim Toft
Pseudo-Differential Operators, Generalized Functions and Asymptotics
Book
03/2015
Birkhäuser
€106.99
Shipment within 10-15 days

Shahla Molahajloo | Stevan Pilipovic | Joachim Toft
Pseudo-Differential Operators, Generalized Functions and Asymptotics
E-Book
02/2013
1st Edition
Birkhäuser
€96.29
Available for download
Content
Preface.- Elliptic Theory for Operators Associated with Diffeomorphisms of Smooth Manifolds.- The Singular Functions of Branching Edge Asymptotics.- The Heat Kernel and Green Function of the Sub-Laplacian on the Heisenberg Group.- Metaplectic Equivalence of the Hierarchical Twisted Laplacian.- The Heat Kernel and Green Function of a Sub-Laplacian on the Hierarchical Heisenberg Group.- Lp-Bounds for Pseudo-Differential Operators on the Torus.- Multiplication Properties in Gelfand-Shilov Pseudo-Differential Calculus.- Operator Invariance.- Initial Value Problems in the Time-Frequency Domain.- Polycaloric Distributions and the Generalized Iterated Heat Operator.- Smoothing Effect and Fredholm Property for First-Order Hyperbolic PDEs.- A Note on Wave-Front Sets of Roumieu Type Ultradistributions.- Ordinary Differential Equations in Algebras of Generalized Functions.- Asymptotically Almost Periodic Generalized Functions.- Wave Equations and Symmetric First-Order Systems in Case of Low Regularity.- Concept of Delta-Shock Type Solutions to Systems of Conservation Laws and the Rankine-Hugoniot Conditions.- Classes of Generalized Functions with Finite Type Regularities.- The Wave Equation with a Discontinuous Coefficient Depending on Time Only: Generalized Solutions and Propagation of Singularities.- Gerenalized Solutions of Abstract Stochastic Problems.- Nonhomogeneous First-Order Linear Malliavin Type Differential Equation.