Linked e-resources
Details
Table of Contents
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
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
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.
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.
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
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.
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.