Analytic D-Modules and Applications

1. Auflage. Softcover version of original hardcover Auflage 1993
ISBN: 978-90-481-4238-5
Verlag: Springer Netherlands

Buch, Englisch, Band 247, 581 Seiten, Paperback, Format (B × H): 170 mm x 244 mm, Gewicht: 1020 g

Reihe: Mathematics and Its Applications

'Et moi,., si favait su comment eo reveoir. je One service mathematics has rendered the n'y serais point all6.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded nonsense'. Tbe series is divergent; therefore we may be EricT. Bell ajle to do something with it O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and nonlineari­ tL es abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sci­ ences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One ser­ vice topology has rendered mathematical physics.'; 'One service logic has rendered computer science.'; 'One service category theory has rendered mathematics.'. All arguably true. And all statements obtainable this way form part of the raison d' etre of this series.

Zielgruppe

Research

Autoren/Hrsg.

Björk, Jan-Erik

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

Inhaltsverzeichnis

I. The sheaf DX and its modules.- II. Operations on D-modules.- III. Holonomic D-modules.- IV. Deligne modules.- V. Regular holonomic D-modules.- VI. b-functions.- VII. Distributions and regular holonomic systems.- VIII. Microdifferential operators.- A:I Derived Categories.- Summary.- A:I.1 The construction of derived categories.- A:I.2. Properties of derived categories.- A:I.3. Injective resolutions.- A:I.4. Spectral sequences.- A:II Sheaf Theory.- Summary.- A:II.1. The category of sheaves.- A:II.2. Operations on sheaves.- A:II.3. The derived category of sheaves.- A:II.4. Flabby sheaves.- A:II.5. Sheaves on paracompact manifolds.- A:II.6. Ringed spaces.- A:II.7. Derived categories of modules.- A:III Filtered rings.- Summary.- A:III.1. Filtered rings.- A:III.2. Filtered sheaves of rings.- A:III.3. Gabber’s Theorem.- A:IV Homological algebra.- Summary.- A:IV.1. Basic facts in homological algebra.- A:IV.2. Auslander regular rings.- A:IV.3. Commutative algebra.- A:IV.4. Filtered Auslander regular rings.- A:V Complex analysis.- Summary.- A:V.2. Analysis on complex manifolds.- A:V.4. The local Milnor fibrations.- A:VI Analytic geometry.- Summary.- A:VI.1. Subanalytic sets.- A:VII Symplectic analysis.- Summary.- A:VII.1. Symplectic algebra.- A:VII:3. Lagrangian varieties.- A:VII.4. Lagrangian varieties in generic position.- References.- List of notations.