Komatsu, H. Kawai :  Boundary values of hyperfunction solutions of linear partial differential equations , Publ.
Malgrange, B. Maslov, V. Sato, M. Tokyo Press, Tokyo, , pp.
Kawai and M. Kashiwara :  On pseudo-differential equations in hyperfunction theory , to appear in Proceedings of the Symposium on Partial Differential Equations held by A. Kashiwara :  Microfunctions and pseudo-differential equations , to appear in the report of Katata symposium. Schwartz, L.
Differential — Operator Solutions for Complex Partial Differential Equations
Paris, Journals Seminars Books Theses Authors. About this book Introduction From the reviews : "Since E. Hille and K. Yoshida established the characterization of generators of C 0 semigroups in the s, semigroups of linear operators and its neighboring areas have developed into a beautiful abstract theory.
- Morrey type function spaces and applications to partial differential equations.
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- Methods of Complex Analysis in Partial Differential Equations with Applications.
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Moreover, the fact that mathematically this abstract theory has many direct and important applications in partial differential equations enhances its importance as a necessary discipline in both functional analysis and differential equations. In my opinion Pazy has done an outstanding job in presenting both the abstract theory and basic applications in a clear and interesting manner. The choice and order of the material, the clarity of the proofs, and the overall presentation make this an excellent place for both researchers and students to learn about C 0 semigroups.
Semigroups of Linear Operators and Applications to Partial Differential Equations
Pazy's decision to give a connected account of the applications to partial differential equations in the last two chapters was a particularly happy one, since it enables one to see what the theory can achieve much better than would the insertion of occasional examples. The chapters achieve a very nice balance between being so easy as to appear disappointing, and so sophisticated that they are incomprehensible except to the expert. Riemannian metrics, Levi-Civita connections, curvature and Jacobi fields, second variation formula, comparison theorems, shortest path, homogeneous spaces, Morse theory and closed geodesics, sphere theorem, finiteness theorem, non-negatively curved spaces, non-positively curves spaces.
Quadratic reciprocity law, p-adic fields, Hilbert symbols, quadratic forms.
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Dirichelt Series, Riemann Zeta function, prime number theorem, modular forms. Free groups and free products, finite generating groups, finite representation groups and their growth properties, polynomial and exponential growth of groups. Basics of knot theory, invariants of knots and links, compositions, Seifert surfaces, Alexander polynomials and Jones polynomials.
Heegard splitting, Dehn surgery of 3-manifolds, Poincare conjecture, foliation theory, fibrations.