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Distributive Lattices and Their Applications in Complex Analysis

Available Formats:
Softcover ISBN: 978-0-8218-3088-8
Product Code: STEKLO/162
82 pp
List Price: $58.00 MAA Member Price:$52.20
AMS Member Price: $46.40 Click above image for expanded view Distributive Lattices and Their Applications in Complex Analysis Available Formats:  Softcover ISBN: 978-0-8218-3088-8 Product Code: STEKLO/162 82 pp  List Price:$58.00 MAA Member Price: $52.20 AMS Member Price:$46.40
• Book Details

Proceedings of the Steklov Institute of Mathematics
Volume: 1621985
MSC: Primary 06; Secondary 32; 46;

Algebraic methods have penetrated deeply into contemporary complex analysis, having an essential influence on both the choice of problems and on the methods for solving them. This monograph deals with the applications of distributive lattices of subspaces to problems in multidimensional complex analysis. The author extends and refines Bogolyubov's “edge-of-the-wedge” theorem, which is formulated as the exactness of a definite homology sequence in various classes of holomorphic functions. He also undertakes a systematic study of two classes of analytic functionals, the so-called Fourier hyperfunctions and the Fourier ultrahyperfunctions, on the basis of distributive lattices of linear subspaces. With this goal in mind, he obtains a homology characterization of distributive lattices of submodules, along with duality formulas for dual lattices of locally convex subspaces. The book is intended for specialists in the theory of functions of several complex variables.