Boundary Value Problems for Operator Differential Equations (Mathematics and its Applications)



Myroslav L. Gorbachuk, "Boundary Value Problems for Operator Differential Equations (Mathematics and its Applications)"
Publisher: | 1990 | ISBN 0792303814 | File type: PDF | 364 pages | 9.6 mb

This volume is devoted largely to the spectral theory of boundary value priblems for (mainly) second order differential equations whose coefficients are unbounded operators in some Hilbert space (differential operator equations). Many differential equations can be written in such a form. A main tool in these studies is the recent extension theory of symmetric operators with arbitrary deficiency index which appears here for the first time in book form.
A theory of boundary values of solutions of abstract differential equations is developed which contains, in particular, the boundary value theory of analytical functions. A great deal of attention is given to the construction and analysis of various spaces of smooth and generalized elements associated with an unbounded closed operator in a Banach space. These spaces of elements constitute natural generalizations of such well-known classical spaces of functions as analytical funcyions, smooth functions of Gevrey class, distributions, ultradistributions, and hyperfunctions. The (abstract) results obtained are applied to, and illustrated by, various classical examples from the theory of boundary values of partial differential equations.
Audience: Researchers and postgraduate students interested in the spectral theory of operators and the theory of partial differential equations.

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