Complex Analysis in One Variable and Riemann Surfaces

Nyhet

Inbunden, Engelska, 2025

1 329 kr

Kommande

By taking advantage of the development of Hilbert space methods in partial differential equations, this textbook provides a much-needed update on complex function theory and Riemann surfaces.In the first five chapters, the authors introduce some background material in complex analysis in one variable using only multivariable calculus.

Produktinformation

Utgivningsdatum2025-12-31
Mått155 x 235 x undefined mm
FormatInbunden
SpråkEngelska
SerieGraduate Texts in Mathematics
Antal sidor550
FörlagSpringer International Publishing AG
ISBN9783031936418

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Mei-Chi Shaw is Emerita professor of mathematics at the University of Notre Dame. Her research interests are in several complex variables, partial differential equations and complex geometry. She is the co-recipient of the 2019 Bergman prize, American Mathematical Society. Charles Stanton is retired from Manchester University and is affiliated with the Department of Mathematics, University of Notre Dame. His research interests are in uniform algebras and complex analysis.

Preface.- 1 Basic properties of holomorphic functions.- 2 Complex integration.- 3 Singularities and the residue theorem.- 4 Holomorphic functions on simply connected domains.- 5 Prescribing zeros and poles.- 6 The inhomogeneous Cauchy-Riemann equation.- 7 Riemann Surfaces.- 8 Harmonic functions and the Dirichlet problem.- 9 The Dirichlet problem: L^2 techniques.- 10 Function theory on compact Riemann surfaces.- 11 The uniformization theorem.- 12 An introduction to several complex variables.- A Compactness in function spaces.- B Hilbert spaces.- C Integral kernels and Fourier series.- D Fourier transforms and the Rellich lemma.- E Distributions and fundamental solutions.- F Cohomology on a Riemann surface.- Bibliography.- Index.