Complex Integration and Cauchy's Theorem
by G. N. Watson
Publisher: Cambridge University Press 1914
Number of pages: 100
This brief monograph by one of the great mathematicians of the early 20th century offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Developing an arithmetical basis that avoids geometrical intuitions, Watson also provides a brief account of the various applications of the theorem to the evaluation of definite integrals.
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by B. Malgrange - Tata Institute of Fundamental Research
Contents: Cauchy's formula and elementary consequences; Reinhardt domains and circular domains; Complex analytic manifolds; Analytic Continuation; Envelopes of Holomorphy; Domains of Holomorphy - Convexity Theory; d''-cohomology on the cube; etc.
by M.-H. Schwartz - Tata Institute of Fundamental Research
Contents: Preliminaries; Some theorems on stratification; Whitney's Theorems (Tangent Cones, Wings, The singular set Sa); Whitney Stratifications and pseudofibre bundles (Pseudo fibre spaces, Obstructions in pseudo-fibrations, etc.).
by K. Chandrasekharan - Tata Institute of Fundamental Research
These notes provide an intorduction to the theory of the Riemann Zeta-function for students who might later want to do research on the subject. The Prime Number Theorem, Hardy's theorem, and Hamburger's theorem are the principal results proved here.
by S. Axler, J. McCarthy, D. Sarason - Cambridge University Press
This volume consists of expository articles on holomorphic spaces. Topics covered are Hardy spaces, Bergman spaces, Dirichlet spaces, Hankel and Toeplitz operators, and a sampling of the role these objects play in modern analysis.