Partial Differential Equations - Aleksei A. Dezin

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Sommaire:
I. Elements of Spectral Theory.- ?0. Introductory Remarks.- ?1. Basic Definitions.- ?2. The Spectrum of an Operator.- ?3. Special Classes of Operators.- II. Function Spaces and Operators Generated by Differentiation.- ?0. Introductory Remarks.- ?1. The Space IH(F).- ?2. Differential Operations and the Maximal Operator.- ?3. The Minimal Operator and Proper Operators.- ?4. Weak and Strong Extensions of Differential Operations.- ?5. Averaging Operators.- ?6. The Identity of Weak and Strong Extensions of Differential Operations.- ?7. W Spaces.- III. Ordinary Differential Operators.- ?0. Introductory Remarks.- ?1. Description of Proper Operators for n = 1..- ?2. The Ordinary Differential Operator of the First Order.- ?3. Birkhoff Theory.- ?4. Supplementary Remarks.- IV. Model Operators.- ?0. Introductory Remarks.- ?1. Tensor Products and Model Operators.- ?2. Operators on the n-Dimensional Torus.- V. First-Order Operator Equations.- ?0. Introductory Remarks.- ?1. The Operator Dt-A; The Spectrum.- ?2. The Operator Dt2013A; Special Boundary Conditions.- ?3. The Operator Dt-k\Classification.- ?4. Operators not Solvable for Dt.- ?5. Differential Properties of the Solutions of Operator Equations, and Related Questions.- 6. Some Operators with Variable Coefficients in the Principal Part.- 7. Concluding Remarks.- VI. Operator Equations of Higher Order.- ?0. Introductory Remarks.- ?1. Second-Order Operator Equations.- ?2. Operator Equations of Higher Order (m 2).- VII. General Existence Theorems for Proper Operators...- ?0. Introductory Remarks.- ?1. Lemma on Restriction of a Domain.- ?2. Existence Theorem for a Proper Operator.- 3. Description of Proper Operators in a Parallelepiped.- VIII. A Special Operational Calculus.- ?0. IntroductoryRemarks.- ?1. Construction of the Operational Calculus.- ?2. Some Examples.- ?3. The Necessity for Restrictions on the Resolvent.- Concluding Remarks.- Appendix 1. On Some Systems of Equations Containing a Small Parameter.- ?1. Formulation of the Problem.- ?2. Truncation of the System.- ?3. The Complete System.- Appendix 2. Further Developments.- References.- Index of Symbols.