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Boundary Value Problems and Singular Pseudo-differential Operators
covers the analysis of pseudo-differential operators on manifolds
with conical points and edges. The standard singular integral
operators on the half-axis as well as boundary value problems on
smooth manifolds are treated as particular cone and wedge theories.
Particular features of the book are:
* A self-contained presentation of the cone pseudo-differential
calculus
* A general method for pseudo-differential analysis on manifolds
with edges for arbitrary model cones in spaces with discrete and
continuous asymptoties
* The presentation of the algebra of boundary value problems with
the transmission property, obtained as a modification of the
general wedge theory
* A new exposition of the pseudo-differential calculus with
operator-valued symbols, based on twisted homogeneity as well as on
parameter-dependent theories and reductions of orders.
The coverage of this book helps to enrich the general theory of
partial differential equations, thus making it essential reading
for researchers and practitioners in mathematics, physics and the
applied sciences. Contents: Preface Pseudo-differential operators
Mellin pseudo-differential operators on manifolds with conical
singularities Pseudo-differential calculus on manifolds with edges
Boundary value problems Bibliography Index
This volume contains the proceedings of the international
conference on " Operator Calculus and Spectral Theory" in
Lambrecht, Germany, Decem- ber 9. - 14. , 1991, sponsored by the
Deutsche Forschungsgemeinschaft, and by the
Karl-Weierstrass-Institute of Mathematics, Berlin. The idea was to
bring together specialists from different areas of modern analysis,
geometry and mathematical physics, in a similar spirit as in the
earlier series of conferences of the Karl-Weierstrass- Institute
(Ludwigsfelde, 1976; Reinhardsbrunn, 1985; Holzhau, 1988;
Breitenbrunn,1990). Berlin, Mainz M. Demuth B. Gramsch B. -W.
Schulze List of talks given in La. brecht. 8. - 14. December 91
Name Title S. Albeverio Some recent deveiopments in Dirichlet forms
and associated processes U. Bunke On the spectral flow of Dirac
operators with negative definite functions as symbols -
applications in probability theory and mathematical physics M.
Combescure Recurrent versus diffusive behaviour for time-dependent
quantum Hamiltonian E. B. Davies Analysis on graphs and
noncommutative geometry M. Demuth On stochastic spectral analysis
and asymptotics for Schrodinger operators P. Duclos A global
approach to the location of quantum resonances v. v. Egorov On
negative spectrum of elliptic operators V. EnB Non-threshold states
of long-range N-body problems B. Gramsch -algebras and microlocal
analysis P. B. Gilkey On the index of geometrical operators for
Riemannian manifolds with boundary B. Helffer Spectral problems in
statistical mechanics R. Hempe I Second order pertubations of
elliptic operators with periodic principal part T. Ichinose On the
Weyl quantized relativistic Hamiltonian V. V.
Die Theorie des NEWToNschen Potentials von Massenverteilungen im
Raum ist eines der altesten Beispiele einer Verbindung von
physikalischer Anschauung und mathematischer Interpretation.
Bedeutende Mathematiker vieler Generationen, wie C. F. GAUSS, H.
POINCARE, D. lIILEERT, N. WIENER haben daran mitgearbeitet. Die
Entwicklung der modernen Potentialtheorie ist auch wesentlich durch
die Arbeiten von G. C. EVANS, M. RIEsz, O. FBOSTMAN, M. V. KELDYs,
M. BRELoT, H. CARTAN, J. DENY, G. CHOQUET, J. L. DooE, H. BAUER, C.
CONSTANTINESCU, V. G. MAz 'JA, B. FUGLEDE und anderen bestimmt
worden. Historische Darstellungen wurden z. B. in [K6], [A30],
[B40] gegeben. Obwohl einige Teile der Potentialtheorie heute als
im wesentlichen abgeschlossen gelten, hat sich die Entwicklung in
den letzten Jahren wieder erheblich verstarkt, seit sich viele
ihrer leistungsfahigen Begriffe und Methoden durch den zunehmenden
Einsatz funktionalanalytischer Methoden auf weite Klassen von
Problemen aus der Theorie der partiellen Differentialgleichungen
anwenden lassen. Daneben sind in der Analysis auch davon
unabhangige Bestrebungen von potentialtheoretischem Charakter zu
beobachten.
This volume presents a systematic and mathematically rigorous
exposition of methods for studying linear partial differential
equations. It focuses on quantization of the corresponding objects
(states, observables and canonical transformations) in the phase
space. The quantization of all three types of classical objects is
carried out in a unified way with the use of a special integral
transform. This book covers recent as well as established results,
treated within the framework of a universal approach. It also
includes applications and provides a useful reference text for
graduate and research-level readers.
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