Series: Applied Mathematical Sciences, Vol. 197
1st ed. 2017, X, 477 p. 4 illus.
Hardcover
ISBN 978-3-319-65261-0
* Each chapter is self-contained and can be read independently
* Content grew from a series of half-semester courses given at
University of Oulu
* Contains material only previously published in scientific journals
* Useful to both students and researchers who have applications in
mathematical physics and engineering sciences
This text serves as an introduction to the modern theory of analysis and differential
equations with applications in mathematical physics and engineering sciences. Having
outgrown from a series of half-semester courses given at University of Oulu, this book
consists of four self-contained parts.
The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical
one-dimensional trigonometric Fourier series with some applications to PDEs and signal
processing. The second part, Fourier Transform and Distributions, is concerned with
distribution theory of L. Schwartz and its applications to the Schrodinger and magnetic
Schrodinger operations. The third part, Operator Theory and Integral Equations, is
devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their
applications to integral equations in such spaces. The fourth and final part, Introduction
to Partial Differential Equations, serves as an introduction to modern methods for classical
theory of partial differential equations.
Complete with nearly 250 exercises throughout, this text is intended for graduate level
students and researchers in the mathematical sciences and engineering.
Series: Springer Proceedings in Mathematics & Statistics, Vol. 207
1st ed. 2017, XIX, 215 p. 6 illus. in color.
Hardcover
ISBN 978-3-319-65180-4
* Provides a unique overview on non-commutative harmonic
analysis on homogeneous spaces with many applicationsCollects
interesting perspectives from several researchers working on
manifold different areasFocuses on analysis, algebra and geometry
and their interconnections
This book provides the latest competing research results on non-commutative harmonic
analysis on homogeneous spaces with many applications. It also includes the most recent
developments on other areas of mathematics including algebra and geometry.
Lie group representation theory and harmonic analysis on Lie groups and on their
homogeneous spaces form a significant and important area of mathematical research.
These areas are interrelated with various other mathematical fields such as number
theory, algebraic geometry, differential geometry, operator algebra, partial differential
equations and mathematical physics.
Keeping up with the fast development of this exciting area of research, Ali Baklouti
(University of Sfax) and Takaaki Nomura (Kyushu University) launched a series of seminars
on the topic, the first of which took place on November 2009 in Kerkennah Islands, the
second in Sousse on December 2011, and the third in Hammamet&
nbsp;on December 2013. The last seminar, which took place on December 18th to 23rd
2015 in Monastir, Tunisia, has promoted further research in all the fields where the
main focus was in the area of Analysis, algebra and geometry and on topics of joint
collaboration of many teams in several corners. Many experts from both countries have
been involved.
Series: Springer Proceedings in Mathematics & Statistics, Vol. 209
1st ed. 2017, VII, 296 p. 18 illus., 6 illus. in@color.
Hardcover
ISBN 978-3-319-66838-3
'This book addresses mathematical problems motivated by various applications in
physics, engineering, chemistry and biology. It gathers the lecture notes from the
mini-course presented by Jean-Christophe Mourrat on the construction of the various
stochastic gbasich terms involved in the formulation of the dynamic O4 theory in three
space dimensions, as well as selected contributions presented at the fourth meeting
on Particle Systems and PDEs, which was held at the University of Minhofs Centre of
Mathematics in December 2015. The purpose of the conference was to bring together
prominent researchers working in the fields of particle systems and partial differential
equations, offering them a forum to present their recent results and discuss their topics of
expertise. The meeting was also intended to present to a vast and varied public, including
young researchers, the area of interacting particle systems, its underlying motivation, and
its relation to partial@differential equations.
The book will be of great interest to probabilists, analysts, and all mathematicians whose
work focuses on topics in mathematical physics, stochastic processes and differential
equations in general, as well as physicists working in statistical mechanics and kinetic
theory.h
Series: Lecture Notes in Mathematics, Vol. 2202
1st ed. 2017, VIII, 211 p. 7 illus.
Softcover
ISBN 978-3-319-67611-1
* Features thorough discussions on well/ill-posedness of the Cauchy
problem for differential operators with double characteristics of noneffectively
hyperbolic type
* Takes a unified approach combining geometrical and microlocal
tools
* Adopts the viewpoint that the Hamilton map and the geometry of
bicharacteristics characterizes the well/ill-posedness of the Cauchy
problem
Combining geometrical and microlocal tools, this monograph gives detailed proofs of
many well/ill-posed results related to the Cauchy problem for differential operators with
non-effectively hyperbolic double characteristics. Previously scattered over numerous
different publications, the results are presented from the viewpoint that the Hamilton
map and the geometry of bicharacteristics completely characterizes the well/ill-posedness
of the Cauchy problem.
A doubly characteristic point of a differential operator P of order m (i.e. one where Pm =
dPm = 0) is effectively hyperbolic if the Hamilton map FPm has real non-zero eigenvalues.
When the characteristics are at most double and every double characteristic is effectively
hyperbolic, the Cauchy problem for P can be solved for arbitrary lower order terms.
If there is a non-effectively hyperbolic characteristic, solvability requires the subprincipal
symbol of P to lie between * PÊj and P Êj , where iÊj are the positive imaginary
eigenvalues of FPm . Moreover, if 0 is an eigenvalue of FPm with corresponding 4 ~
4 Jordan block, the spectral structure of FPm is insufficient to determine whether the
Cauchy problem is well-posed and the behavior of bicharacteristics near the doubly
characteristic manifold plays a crucial role.