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The asymptotic analysis has obtained new impulses with the general
development of various branches of mathematical analysis and their
applications. In this book, such impulses originate from the use of
slowly varying functions and the asymptotic behavior of generalized
functions. The most developed approaches related to generalized
functions are those of Vladimirov, Drozhinov and Zavyalov, and that
of Kanwal and Estrada. The first approach is followed by the
authors of this book and extended in the direction of the
S-asymptotics. The second approach - of Estrada, Kanwal and Vindas
- is related to moment asymptotic expansions of generalized
functions and the Ces'aro behavior. The main features of this book
are the uses of strong methods of functional analysis and
applications to the analysis of asymptotic behavior of solutions to
partial differential equations, Abelian and Tauberian type theorems
for integral transforms as well as for the summability of Fourier
series and integrals. The book can be used by applied
mathematicians, physicists, engineers and others who use classical
asymptotic methods and wish to consider non-classical objects
(generalized functions) and their asymptotics now in a more
advanced setting.
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.
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.
This book gathers peer-reviewed contributions representing modern
trends in the theory of generalized functions and
pseudo-differential operators. It is dedicated to Professor Michael
Oberguggenberger (Innsbruck University, Austria) in honour of his
60th birthday. The topics covered were suggested by the ISAAC Group
in Generalized Functions (GF) and the ISAAC Group in
Pseudo-Differential Operators (IGPDO), which met at the 9th ISAAC
congress in Krakow, Poland in August 2013. Topics include Columbeau
algebras, ultra-distributions, partial differential equations,
micro-local analysis, harmonic analysis, global analysis, geometry,
quantization, mathematical physics, and time-frequency analysis.
Featuring both essays and research articles, the book will be of
great interest to graduate students and researchers working in
analysis, PDE and mathematical physics, while also offering a
valuable complement to the volumes on this topic previously
published in the OT series.
This book gathers peer-reviewed contributions representing modern
trends in the theory of generalized functions and
pseudo-differential operators. It is dedicated to Professor Michael
Oberguggenberger (Innsbruck University, Austria) in honour of his
60th birthday. The topics covered were suggested by the ISAAC Group
in Generalized Functions (GF) and the ISAAC Group in
Pseudo-Differential Operators (IGPDO), which met at the 9th ISAAC
congress in Krakow, Poland in August 2013. Topics include Columbeau
algebras, ultra-distributions, partial differential equations,
micro-local analysis, harmonic analysis, global analysis, geometry,
quantization, mathematical physics, and time-frequency analysis.
Featuring both essays and research articles, the book will be of
great interest to graduate students and researchers working in
analysis, PDE and mathematical physics, while also offering a
valuable complement to the volumes on this topic previously
published in the OT series.
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