Unpublished Manuscripts: from 1951 to 2007 [1st ed. 2018] 3319698494, 9783319698496

Table of contents :
Foreword
Contents
Origin of the Manuscripts
1 APPLICATIONS OF HELLYS THEOREM TO ESTIMATES OF TCHEBYCHEFF TYPE
A generalization of a theorem by Helly on convex bodies.
Two theorems concerning generalized polynomials.
Tschebyscheffs approximation theorem.
2 AN ISOPERIMETRIC INEQUALITY IN HOMOGENEOUS FINSLER SPACES
3 ON BEST APPROXIMATION IN L1
4 PETROWSKYS 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
References
6 INEQUALITIES BETWEEN NORMAL AND TANGENTIAL DERIVATIVES OF HARMONIC FUNCTIONS
References
7 THE DIRICHLET PROBLEM IN A MAXIMAL OPEN SET
References
8 THE DIFFUSION APPROXIMATIONIN NEUTRON TRANSPORT THEORY
Introduction.
An a priori inequality.
The asymptotic condition for subcriticality.
The limit of the solution of (1).
References
9 SOME TAUBERIAN THEOREMS OF LEWITAN
Onesided Bohr inequality.
SOME VARIANTS OF AN INEQUALITY DUE TO H. BOHR
10 ELECTROMAGNETIC WAVE PROPAGATION OVER GROUND WITH SMALL INHOMOGENEITIES IN THE ELECTRICAL CONSTANTS
1. Introduction.
2. Maxwells 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. Valentines extension theorem.
References
13 THE WORK OF CARLESON AND HOFFMAN ONBOUNDED ANALYTIC FUNCTIONS IN THE DISC
References
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.
24. Unique continuation.
25. Unique continuation.
26. Nonexistence theorems.
27. Domination.
28. Multipliers on Fourier transforms.
29. Asymptotic properties of eigenfunctions, second order case.
Comments added in November 1997
15 REMARKS ON CONVEXITY WITH RESPECTTO OPERATORS OF REAL PRINCIPAL TYPE
0. Introduction.
1. A sufficient condition for P-convexity.
2. Construction of local null solutions.
3. A uniqueness theorem.
References
16 FOURIER MULTIPLIERS WITH SMALL NORM
References
17 THE COSINE THEOREM ON A SURFACE AND THE NOTION OF CURVATURE
0. Introduction.
2. Spherical triangles.
3. Geodesic triangles on surfaces.
4. The higher dimensional case.
Appendix A: Geodesics.
Appendix B: Higher order approximations.
References
18 CORRECTION TO MY PAPER ON SOBOLEV SPACES ASSOCIATED WITH SOME LIE ALGEBRAS
References
19 GRDINGS INEQUALITY DURING THREE DECADES
1. The original result.
2. The sharp Garding inequality.
3. Melins inequality.
4. The Fefferman-Phong estimates.
5. The sharp Garding inequality for paradifferential operators.
References
20 SYMPLECTIC GEOMETRY AND DIFFERENTIAL EQUATIONS
0. Introduction.
1. Classical mechanics.
2. Hamilton-Jacobi theory.
3. Propagation of singularities.
4. Solvability of differential equations.
References
21 GENERAL MEHLER FORMULAS AND THE WEYL CALCULUS
Appendix: Mehlers Dirichlet problem.
References
22 GUIDE TO THE MATHEMATICAL MODELS AT THE DEPARTMENT OF MATHEMATICS IN LUND
1. Introduction.
2. Quadratic surfaces.
3. Local classification of surfaces.
4. Cubic surfaces.
References
23 THE PROOF OF THE NIRENBERG-TREVES CONJECTUREACCORDING TO N. DENCKER AND N. LERNER
1. Introduction.
2. Metrics and weights.
3. Pseudodifferential calculus.
4. A priori estimates for model operators.
5. The sufficiency of condition ( ).
6. Some open problems on solvability.
References
24 LOWER BOUNDS FOR SUBELLIPTIC OPERATORS
0. Introduction.
1. Localization.
2. The test estimates.
3. Local and global estimates.
4. A precise commutator estimate.
References
25 APPROXIMATION OF SOLUTIONS OF CONSTANT COEFFICIENT BOUNDARY PROBLEMS AND OF ENTIRE FUNCTIONS
1. Introduction.
2. A division algorithm.
3. The annihilator of the exponential solutions.
4. Gaussian regularization.
5. The case of a single boundary operator.
6. Approximation of entire functions of exponential type.
Appendix.
References
Autobiography, and Looking Forward from ICM 1962
AUTOBIOGRAPHY OF LARS HORMANDER
LOOKING FORWARD FROM ICM 1962
1. Introduction
2. Pseudodifferential Operators and The Wave Front Set
3. Fourier Intergral Operators
4. Hypoellipticity
5. Solvability and Propagation of Singularities
6. Holmgren's Uniqueness Theorem
7. Analytic Hypoellipticity and Propagation of Analytic Singularities
8. Carleman Estimates
9. Spectral Asymptotics
References
Complete Mathematical Bibliography of Lars Hrmander
Published papers
Published books
Lecture notes