Yu.L. Dalecky, S. V. Fomin

Measures and Differential Equations in Infinite-Dimensional Space

• Broschiertes Buch

Produktbeschreibung

lEt moi, .... si j'avait Sll comment en revenir, One service mathematics has rendered the human race. It has put common sense back je n'y serais point aile:' where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded 0- sense'. The series is divergent; therefore we may be Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d 'e1re of this series.

---

Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.

Produktdetails

• Mathematics and its Applications .76
• Verlag: Springer / Springer Netherlands
• Artikelnr. des Verlages: 978-94-010-5148-4
• Softcover reprint of the original 1st ed. 1991
• Seitenzahl: 356
• Erscheinungstermin: 26. Oktober 2012
• Englisch
• Abmessung: 235mm x 155mm x 20mm
• Gewicht: 545g
• ISBN-13: 9789401051484
• ISBN-10: 9401051488
• Artikelnr.: 39152019

Inhaltsangabe

I. Measures and quasimeasures. Integration.- 1. Realvalued measures on algebras of sets.- 2. Cylinder sets and cylindrical functions.- 3. Quasimeasures. Integration.- 4. Supplement: Some notions related to the topology of linear spaces.- 5. Chapter I: Supplementary remarks and historical comments.- II. Gaussian measures in Hilbert space.- 1. Gaussian measures in finite-dimensional spaces.- 2. Gaussian measures in Hilbert space.- 3. Measurable linear functionals and operators.- 4. Absolute continuity of Gaussian measures.- 5. Fourier-Wiener transformation.- 6. Complexvalued Gaussian quasimeasures.- 7. Chapter II: Supplementary re marks and historical comments.- III. Measures in linear topological spaces.- 1. ?-additivity conditions for nonnegative cylindrical measures in the space X' dual to a locally convex space X.- 2. Sequences of Radon measures.- 3. Chapter III: Supplementary remarks and historical comments.- IV. Differentiable measures and distributions.- 1. Differentiable functions, differentiable expressions.- 2. Differentiable measures.- 3. Distributions and generalized functions.- 4. Positive definiteness. Quasi-invariant distributions and bidistributions.- 5. Chapter IV: Supplementary remarks and historical comments.- V. Evolution differential equations.- 1. Weak solutions of evolution equations.- 2. Second order equations with variable coefficient.- 3. Chapter V: Supplementary remarks and historical comments.- VI. Integration in path space.- 1. Markov quasimeasures.- 2. Evolution families of operators.- 3. Linear evolution families and functional integrals.- 4. Nonlinear evolution families, and integrals in branching path space.- 5. Chapter VI: Supplementary remarks and historical comments.- VII. Probabilistic representations of solutions of parabolicequations and systems.- 1. Wiener process. Stochastic integrals.- 2. Stochastic differential equations.- 3. Operator multiplicative functionals and the evolution families determined by them.- 4. The Cauchy problem for second order parabolic systems.- 5. Chapter VII: Supplementary remarks and historical comments.- VIII. Smooth measures.- 1. Admissible operators.- 2. Admissibility of differential operators.- 3. Absolute continuity of smooth measures.- 4. Maps of spaces and admissible operators.- 5. Biorthogonal systems in L2(X, ?).- 6. Chapter VIII: Supplementary remarks and historical comments.- Supplement to chapters IV-V.- 1. Essentially infinite-dimensional elliptic operators.- 2. Properties of essentially infinite-dimensional elliptic operators, and solutions of the corresponding Cauchy problem.- 3. Existence of solutions of the Cauchy problem.- 4. Supplementary remarks and historical comments.- Supplement to chapter VII.- 1. Supplementary remarks and historical comments.