Secure CheckoutPersonal information is secured with SSL technology.
Free ShippingFree global shipping
No minimum order.
Treatise on Analysis, Volume 10–VII provides information pertinent to the fundamental aspects of linear functional equations. This book discusses the problems dealing with functional equations of scalar or of vectors.
Comprised of one chapter, this volume begins with a description and study of the primary concepts and tools that have prompted the progress in the study of linear partial differential equations. This text then explains the importance of the integral operators. The reader is also introduced to integral operators that operate not only on vector function, but also on sections of vector bundles. This book discusses as well the applications of the differential operators to spectral theory.
This book is a valuable resource for mathematicians.
Chapter XXIII Linear Functional Equations
Part One : Pseudodifferential Operators
1. Integral Operators
2. Integral Operators of Proper Type
3. Integral Operators on Vector Bundles
4. Density Bundle and Kernel Sections
5. Bounded Sections
6. Volterra Operators
7. Carleman Operators
8. Generalized Eigenfunctions
9. Kernel Distributions
10. Regular Kernel Distributions
11. Smoothing Operators and Composition of Operators
12. Wave Front of a Distribution
13. Convolution Equations
14. Elementary Solutions
15. Existence and Uniqueness Problems for Systems of Linear Partial Differential Equations
16. Operator Symbols
17. Oscillating Integrals
18. Lax-Maslov Operators
19. Pseudodifferential Operators
20. Symbol of a Pseudodifferential Operator of Proper Type
21. Matrix Pseudodifferential Operators
22. Parametrix of Elliptical Operators on an Open Subset of Rn
23. Pseudodifferential Operators in Hs0(X) Spaces
24. Classical Dirichlet Problem and Coarse Dirichlet Problem
25. The Green Operator
26. Pseudodifferential Operators on a Manifold
27. Adjoint of a Pseudodifferential Operator on a Manifold. Composition of Two Pseudodifferential Operators on a Manifold
28. Extension of Pseudodifferential Operators to Distribution Sections
29. Principal Symbols
30. Parametrix of Elliptic Operators on Manifolds
31. Spectral Theory of Hermitian Elliptic Operators : I. Self-Adjoint Extensions and Boundary Conditions
32. Spectral Theory of Hermitian Elliptic Operators : II. Generalized Eigenfunctions
33. Essentially Self-Adjoint Pseudodifferential Operators : I. Hermitian Convolution Operators on Rn
34. Essentially Self-Adjoint Pseudodifferential Operators : II. Atomic Spectra
35. Essentially Self-Adjoint Pseudodifferential Operators : III. Hermitian Elliptic Operators on a Compact Manifold
36. Invariant Differential Operators
37. Differential Properties of Spherical Functions
38. Example : Spherical Harmonics
- No. of pages:
- © Academic Press 1988
- 28th November 1988
- Academic Press
- eBook ISBN:
Department of Mathematics, Columbia University, New York, New York
Elsevier.com visitor survey
We are always looking for ways to improve customer experience on Elsevier.com.
We would like to ask you for a moment of your time to fill in a short questionnaire, at the end of your visit.
If you decide to participate, a new browser tab will open so you can complete the survey after you have completed your visit to this website.
Thanks in advance for your time.