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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Pseudo-Differential Operators, Singularities, Applications (Paperback, Softcover reprint of the original 1st ed. 1997)
Loot Price: R2,460
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Pseudo-Differential Operators, Singularities, Applications (Paperback, Softcover reprint of the original 1st ed. 1997)
Series: Operator Theory: Advances and Applications, 93
Expected to ship within 18 - 22 working days
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Pseudo-differential operators belong to the most powerful tools in
the analysis of partial differential equations. Basic achievements
in the early sixties have initiated a completely new understanding
of many old and important problems in analy- sis and mathematical
physics. The standard calculus of pseudo-differential and Fourier
integral operators may today be considered as classical. The
development has been continuous since the early days of the first
essential applications to ellip- ticity, index theory, parametrices
and propagation of singularities for non-elliptic operators,
boundary-value problems, and spectral theory. The basic ideas of
the calculus go back to Giraud, Calderon, Zygmund, Mikhlin,
Agranovich, Dynin, Vishik, Eskin, and Maslov. Subsequent progress
was greatly stimulated by the classical works of Kohn, Nirenberg
and Hormander. In recent years there developed a new vital interest
in the ideas of micro- local analysis in connection with analogous
fields of applications over spaces with singularities, e.g. conical
points, edges, corners, and higher singularities. The index theory
for manifolds with singularities became an enormous challenge for
analysists to invent an adequate concept of ellipticity, based on
corresponding symbolic structures. Note that index theory was
another source of ideas for the later development of the theory of
pseudo-differential operators. Let us mention, in particular, the
fundamental contributions by Gelfand, Atiyah, Singer, and Bott.
General
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