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BL
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| Record Number
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864154
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| Main Entry
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Hörmander, Lars
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| Title & Author
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Unpublished manuscripts : : from 1951 to 2007 /\ Lars Hörmander.
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| Publication Statement
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Cham, Switzerland :: Springer,, 2018.
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| Page. NO
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1 online resource (x, 357 pages)
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| ISBN
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3319698494
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: 3319698508
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: 9783319698496
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: 9783319698502
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9783319698496
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| Bibliographies/Indexes
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Includes bibliographical references.
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| Contents
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Intro; Foreword; Contents; Origin of the Manuscripts; 1 APPLICATIONS OF HELLY'S THEOREM TO ESTIMATES OF TCHEBYCHEFF TYPE; A generalization of a theorem by Helly on convex bodies.; Two theorems concerning generalized polynomials.; Tschebyscheff's approximation theorem.; 2 AN ISOPERIMETRIC INEQUALITY IN HOMOGENEOUS FINSLER SPACES; 3 ON BEST APPROXIMATION IN L1; 4 PETROWSKY'S L2 ESTIMATES FOR HYPERBOLIC SYSTEMS; 1. Introduction.; 2. Translation to pseudodifferential calculus.; 3. The original proofs.; References; 5 PROOF OF THE EXISTENCE OF FUNDAMENTAL SOLUTIONS AND OF SOME INEQUALITIES
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11. The uniqueness of the Cauchy problem. 12. Non-elliptic boundary problems.; 13. The exactness of the Spencer sequence.; 14. Universal hypoellipticity.; 15. Boundary problems for non-elliptic operators.; 16. Approximation theorem for boundary problems.; 17. Analytic continuation of solutions of elliptic boundary problems.; 18. Continuation of solutions of boundary problems.; 19. Mixed problems for hyperbolic equations.; 20. Asymptotic properties of eigenfunctions.; 21. Lp theory of the?̄ operator.; 22. Division of distributions.; 23. Asymptotic behavior of Fourier-type integrals.
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13 THE WORK OF CARLESON AND HOFFMAN ONBOUNDED ANALYTIC FUNCTIONS IN THE DISCReferences; 14 SOME PROBLEMS CONCERNING LINEAR PARTIAL DIFFERENTIAL EQUATIONS; 1. Existence of linear right inverse.; 2. Existence of solutions for real analytic right hand side.; 3. Properties of the comparison relation.; 4. Singular supports of solutions.; 5. Admissible lower order terms in a hyperbolic operator.; 6. Supports of fundamental solutions.; 7. Regularity of fundamental solutions.; 8. Global uniqueness theorems.; 9. Solvability.; 10. Pseudodifferential operators related to operators of principal type.
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2. Maxwell's equations in a homogeneous space. 3. Reflection against a homogeneous half space.; References; 11 CLASSES OF INFINITELY DIFFERENTIABLE FUNCTIONS; 1. Definitions and general properties.; 2. The Denjoy-Carleman theorem.; 3. Interpolation in classes of infinitely differentiable functions.; 4. Division in classes of infinitely differentiable functions.; 12 APPROXIMATION ON TOTALLY REAL MANIFOLDS; 1. Introduction.; 2. Local approximation.; 3. Global approximation.; 4. Valentine's extension theorem.; References
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| Abstract
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This book presents, for the first time, the unpublished manuscripts of Lars Hörmander, written between 1951 and 2007. Hörmander himself organised the manuscripts and also wrote the notes explaining their origins, presenting the material in the form he fully intended it to be published in. As his daughter, Sofia Broström, mentions in the Foreword, towards the end of his life, Hörmander "carefully went through his unpublished manuscripts, checking and revising each of them with his very critical eye, deciding what should be kept for posterity and what should be thrown out". He also compiled the complete bibliography of all his published mathematical works that is included at the end of the present book. Of both historical and mathematical value, the contents of this book will undoubtedly inspire mathematicians of different horizons.--
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| Subject
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Hörmander, Lars.
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| Subject
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Differential equations.
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Differential equations.
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MATHEMATICS-- Calculus.
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| Subject
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MATHEMATICS-- Mathematical Analysis.
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| Dewey Classification
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515/.35
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| LC Classification
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QA371.H67 2018
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