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Complexes of Differential Operators (Paperback, Softcover reprint of the original 1st ed. 1995)
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Complexes of Differential Operators (Paperback, Softcover reprint of the original 1st ed. 1995)
Series: Mathematics and Its Applications, 340
Expected to ship within 10 - 15 working days
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This book gives a systematic account of the facts concerning
complexes of differential operators on differentiable manifolds.
The central place is occupied by the study of general complexes of
differential operators between sections of vector bundles. Although
the global situation often contains nothing new as compared with
the local one (that is, complexes of partial differential operators
on an open subset of ]Rn), the invariant language allows one to
simplify the notation and to distinguish better the algebraic
nature of some questions. In the last 2 decades within the general
theory of complexes of differential operators, the following
directions were delineated: 1) the formal theory; 2) the existence
theory; 3) the problem of global solvability; 4) overdetermined
boundary problems; 5) the generalized Lefschetz theory of fixed
points, and 6) the qualitative theory of solutions of
overdetermined systems. All of these problems are reflected in this
book to some degree. It is superfluous to say that different
directions sometimes whimsically intersect. Considerable attention
is given to connections and parallels with the theory of functions
of several complex variables. One of the reproaches avowed
beforehand by the author consists of the shortage of examples. The
framework of the book has not permitted their number to be
increased significantly. Certain parts of the book consist of
results obtained by the author in 1977-1986. They have been
presented in seminars in Krasnoyarsk, Moscow, Ekaterinburg, and N
ovosi birsk.
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