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 Fréchet 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.
Derived Functors in Functional Analysis
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Key Phrases - Statistically Improbable Phrases (SIPs):
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projective spectra, inductive spectrum, convex spectra, projective limit functor, projective spectrum, many injective objects, ultradifferentiable functions, complete locally convex spaces, reduced spectra, spectral maps, exact complex, complemented subspace, countable case, closed neighbourhoods, projective limits, derived functors, convex topology, representing spectrum, continuous linear maps, injective resolution, open mapping theorem, exact rows, inductive limit, exact sequence, group topology New!
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projective spectra, inductive spectrum, convex spectra, projective limit functor, projective spectrum, many injective objects, ultradifferentiable functions, complete locally convex spaces, reduced spectra, spectral maps, exact complex, complemented subspace, countable case, closed neighbourhoods, projective limits, derived functors, convex topology, representing spectrum, continuous linear maps, injective resolution, open mapping theorem, exact rows, inductive limit, exact sequence, group topology New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 28
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45
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- Continuous Bounded Cohomology of Locally Compact Groups (Lecture Notes in Mathematics) by Nicolas Monod in Back Matter
- The Decomposition of Primes in Torsion Point Fields (Lecture Notes in Mathematics) by Clemens Adelmann in Back Matter
- Grothendieck Duality and Base Change (Lecture Notes in Mathematics) by Brian Conrad in Back Matter
- Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids (Lecture Notes in Mathematics) by Martin Fuchs in Back Matter
- Introduction to Algebraic Independence Theory (Lecture Notes in Mathematics) by Yuri V. Nesterenko in Back Matter
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- Geometric Curve Evolution and Image Processing (Lecture Notes in Mathematics) by Frédéric Cao in Back Matter
- Big Queues (Lecture Notes in Mathematics) by Ayalvadi J. Ganesh in Back Matter
- Geometric Aspects of Functional Analysis: Israel Seminar 2001-2002 (Lecture Notes in Mathematics) by Vitali D. Milman in Back Matter
- The Valuative Tree (Lecture Notes in Mathematics) by Charles Favre in Back Matter
- Geometry of Müntz Spaces and Related Questions (Lecture Notes in Mathematics) by Vladimir I. Gurariy in Back Matter
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