Analytic Extension Formulas and their Applications [Paperback]

Analytic Extension is a mysteriously beautiful property of analytic functions. With this point of view in mind the related survey papers were gathered from various fields in analysis such as integral transforms, reproducing kernels, operator inequalities, Cauchy transform, partial differential equations, inverse problems, Riemann surfaces, Euler-Maclaurin summation formulas, several complex variables, scattering theory, sampling theory, and analytic number theory, to name a few.
Audience: Researchers and graduate students in complex analysis, partial differential equations, analytic number theory, operator theory and inverse problems.Analytic Extension is a mysteriously beautiful property of analytic functions. With this point of view in mind the related survey papers were gathered from various fields in analysis such as integral transforms, reproducing kernels, operator inequalities, Cauchy transform, partial differential equations, inverse problems, Riemann surfaces, Euler-Maclaurin summation formulas, several complex variables, scattering theory, sampling theory, and analytic number theory, to name a few.
Audience: Researchers and graduate students in complex analysis, partial differential equations, analytic number theory, operator theory and inverse problems.Preface. 1. Extending holomorphic functions from subvarieties; K. Adachi. 2. Representations of analytic functions on typical domains in terms of local values and truncation error estimates; K. Amano, et al. 3. Uniqueness in determining damping coefficients in hyperbolic equations; A.L. Bukhgeim, et al. 4. Analytic continuation of Cauchy and exponential transforms; B. Gustafsson, M. Putinar. 5. Analytic function spaces and their applications to nonlinear evolution equations; N. Hayashi. 6. A sampling principle associated with Saitoh's fundamental theory of linear transformations; J.R. Higgins. 7. The enclosure methlw