دانلود کتاب Seminar on Singularities of Solutions of Linear Partial Differential Equations. (AM-91), Volume 91

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CONTENTS\nPREFACE\nSPECTRAL ANALYSIS OF SINGULARITIES\n 1. Introduction\n 2. Definition and basic properties of the singular spectrum\n 3. The non-characteristic regularity theorem\n 4. Pseudo-differential operators\n 5. Bicharacteristics and symplectic geometry\n 6. Fourier integral operators corresponding to canonical transformations\n 7. Further equivalence theorems\n 8. Propagation of singularities and semi-global existence theorems for pseudo-differential operators satisfying condition (P)\nFOURIER INTEGRAL OPERATORS WITH COMPLEX PHASE FUNCTIONS\n 0. Introduction\n 1. Local study\n 2. Lagrangean manifolds associated to phase functions\n 3. Global definition of Fourier integral distributions\n 4. Fourier integral operators\n 5. Application to the exponential of a pseudo-differential operator\nHYPOELLIPTIC OPERATORS WITH DOUBLE CHARACTERISTICS\n 1. Conditions for hypoellipticity\n 2. The asymptotic behavior of the eigenvalues\nDIFFERENTIAL BOUNDARY VALUE PROBLEMS OF PRINCIPAL TYPE\n 1. Introduction\n 2. Examples\n 3. Symplectic geometry\n 4. Pseudo-differential operators\n 5. Fourier integral operators\n 6 . Normal forms\n 7. Other boundary conditions\n 8. Higher-order tangency\n 9. Example (2.3) again\nPROPAGATION OF SINGULARITIES FOR A CLASS OF OPERATORS WITH DOUBLE CHARACTERISTICS\n 0. Introduction\n 1. Statement of results\n 2. Reduction to canonical form\n 3. A simple example\n 4. Results independent of the lower order terms\n 5. Results depending on the lower order terms\nSUBELLIPTIC OPERATORS\n 1. Introduction\n 2. The Taylor expansion of the principal symbol\n 3. Necessary conditions for subellipticity\n 4. Local properties of the principal symbol\n 5. Estimates for the localized operators\n 6. Proof of the sufficiency in Theorem 3.4\n 7. Calculus lemmas\n 8. Concluding remarks\nLACUNAS AND TRANSMISSIONS\n 1. Sharp fronts\n 2. Transmissions\n 3. Boundary value problems\n 4. Symmetry of the elementary solution of a hyperbolic equation\n 5. Further developments\nSOME CLASSICAL THEOREMS IN SPECTRAL THEORY REVISITED\n 0. Introduction\n 1. The lattice point problem\n 2. Weyl-type formulas\n 3. Szegö-type formulas I\n 4. Szegö-type formulas II\nA SZEGÖ THEOREM AND COMPLETE SYMBOLIC CALCULUS FOR PSEUDO-DIFFERENTIAL OPERATORS\n 1. Introduction\n 2. Pseudo-differential families in R^n\n 3. The half-space problem\n 4. Pseudo-differential operators on manifolds\n 5. The heat expansion\n 6. Functional calculus