Lecture Notes in Mathematics : Lecture Notes in Mathematics - Jochen Wengenroth

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Lecture Notes in Mathematics

By: Jochen Wengenroth

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Paperback | 10 December 2002

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148 Pages

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The text contains for the first time in book form the state of the art of homological methods in functional analysis like characterizations of the vanishing of the derived projective limit functor or the functors Ext¹ (E, F) for Fr©chet and more general spaces. The researcher in real and complex analysis finds powerful tools to solve surjectivity problems e.g. on spaces of distributions or to characterize the existence of solution operators.
The requirements from homological algebra are minimized: all one needs is summarized on a few pages. The answers to several questions of V.P. Palamodov who invented homological methods in analysis also show the limits of the program.

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Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Algebra Mathematical Foundation Set Theory Differential Calculus & Equations Geometry Algebraic Geometry

Introduction	p. 12
Notions from homological algebra	p. 72
Derived Functors	p. 72
The category of locally convex spaces	p. 133
The projective limit functor for countable spectra	p. 173
Projective limits of linear spaces	p. 173
The Mittag-Leffler procedure	p. 233
Projective limits of locally convex spaces	p. 383
Some Applications	p. 503
The Mittag-Leffler theorem	p. 503
Separating singularities	p. 513
Surjectivity of the Cauchy-Riemann operator	p. 513
Surjectivity of P(D) on spaces of smooth functions	p. 523
Surjectivity of P(D) the space of distributions	p. 523
Differential operators for ultradifferentiable functions of Roumieu type	p. 544
Uncountable projective spectra	p. 594
Projective spectra of linear spaces	p. 594
Insertion: The completion functor	p. 684
Projective spectra of locally convex spaces	p. 705
The derived functors of Hom	p. 775
Extk in the category of locally convex spaces	p. 775
Splitting theory for Frèchet spaces	p. 865
Splitting in the category of (PLS)-spaces	p. 966
Inductive spectra of locally convex spaces	p. 1097
The duality functor	p. 119
References	p. 129
Index
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Lecture Notes in Mathematics

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