Ebook: Analytic Extension Formulas and their Applications

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.

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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.

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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.
Content:
Front Matter....Pages i-vii
Extending Holomorphic Functions from Subvarieties....Pages 1-14
Representations of Analytic Functions on Typical Domains in Terms of Local Values and Truncation Error Estimates....Pages 15-25
Uniqueness in Determining Damping Coefficients in Hyperbolic Equations....Pages 27-46
Analytic Continuation of Cauchy and Exponential Transforms....Pages 47-57
Analytic Function Spaces and their Applications to Nonlinear Evolution Equations....Pages 59-72
A Sampling Principle Associated with Saitoh’s Fundamental Theory of Linear Transformations....Pages 73-86
The Enclosure Method and its Applications....Pages 87-103
On Analytic Properties of a Multiple L-Function....Pages 105-122
Multi-dimensional Inverse Scattering Theory....Pages 123-167
Holomorphic Spaces Related to Orthogonal Polynomials and Analytic Continuation of Functions....Pages 169-187
Extension and Division on Complex Manifolds....Pages 189-206
Analytic Extension Formulas, Integral Transforms and Reproducing Kernels....Pages 207-232
Analytic Continuation beyond the Ideal Boundary....Pages 233-250
Justification of a Formal Derivation of the Euler-Maclaurin Summation Formula....Pages 251-261
Extension of L?wner-Heinz Inequality Via Analytic Continuation....Pages 263-270
The Calogero-Moser Model, the Calogero Model and Analytic Extension....Pages 271-285
Back Matter....Pages 287-287

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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.
Content:
Front Matter....Pages i-vii
Extending Holomorphic Functions from Subvarieties....Pages 1-14
Representations of Analytic Functions on Typical Domains in Terms of Local Values and Truncation Error Estimates....Pages 15-25
Uniqueness in Determining Damping Coefficients in Hyperbolic Equations....Pages 27-46
Analytic Continuation of Cauchy and Exponential Transforms....Pages 47-57
Analytic Function Spaces and their Applications to Nonlinear Evolution Equations....Pages 59-72
A Sampling Principle Associated with Saitoh’s Fundamental Theory of Linear Transformations....Pages 73-86
The Enclosure Method and its Applications....Pages 87-103
On Analytic Properties of a Multiple L-Function....Pages 105-122
Multi-dimensional Inverse Scattering Theory....Pages 123-167
Holomorphic Spaces Related to Orthogonal Polynomials and Analytic Continuation of Functions....Pages 169-187
Extension and Division on Complex Manifolds....Pages 189-206
Analytic Extension Formulas, Integral Transforms and Reproducing Kernels....Pages 207-232
Analytic Continuation beyond the Ideal Boundary....Pages 233-250
Justification of a Formal Derivation of the Euler-Maclaurin Summation Formula....Pages 251-261
Extension of L?wner-Heinz Inequality Via Analytic Continuation....Pages 263-270
The Calogero-Moser Model, the Calogero Model and Analytic Extension....Pages 271-285
Back Matter....Pages 287-287
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