Analytic Extension Formulas and their Applications

1. Front Matter

   Pages i-vii

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2. Extending Holomorphic Functions from Subvarieties

   • Kenzō Adachi

   Pages 1-14

3. Representations of Analytic Functions on Typical Domains in Terms of Local Values and Truncation Error Estimates

   • K. Amano, M. Asaduzzaman, T. Ooura, S. Saitoh

   Pages 15-25

4. Uniqueness in Determining Damping Coefficients in Hyperbolic Equations

   • A. L. Bukhgeim, J. Cheng, V. Isakov, M. Yamamoto

   Pages 27-46

5. Analytic Continuation of Cauchy and Exponential Transforms

   • Björn Gustafsson, Mihai Putinar

   Pages 47-57

6. Analytic Function Spaces and their Applications to Nonlinear Evolution Equations

   • Nakao Hayashi

   Pages 59-72

7. A Sampling Principle Associated with Saitoh’s Fundamental Theory of Linear Transformations

   • J. R. Higgins

   Pages 73-86

8. The Enclosure Method and its Applications

   • Masaru Ikehata

   Pages 87-103

9. On Analytic Properties of a Multiple L-Function

   • Hideaki Ishikawa

   Pages 105-122

10. Multi-dimensional Inverse Scattering Theory

    • Hiroshi Isozaki

    Pages 123-167

11. Holomorphic Spaces Related to Orthogonal Polynomials and Analytic Continuation of Functions

    • Dmitri Karp

    Pages 169-187

12. Extension and Division on Complex Manifolds

    • Takeo Ohsawa

    Pages 189-206

13. Analytic Extension Formulas, Integral Transforms and Reproducing Kernels

    • Saburou Saitoh

    Pages 207-232

14. Analytic Continuation beyond the Ideal Boundary

    • M. Shiba

    Pages 233-250

15. Justification of a Formal Derivation of the Euler-Maclaurin Summation Formula

    • Masaaki Sugihara

    Pages 251-261

16. Extension of Löwner-Heinz Inequality Via Analytic Continuation

    • Mitsuru Uchiyama

    Pages 263-270

17. The Calogero-Moser Model, the Calogero Model and Analytic Extension

    • Shuji Watanabe

    Pages 271-285

18. 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.

• Complex analysis
• Operator theory
• Riemann surfaces
• analytic function
• hyperbolic equation
• integral transform
• partial differential equation
• scattering theory
• partial differential equations

• Gunma University, Japan

  Saburou Saitoh

• Science University of Tokyo, Japan

  Nakao Hayashi

• University of Tokyo, Japan

  Masahiro Yamamoto

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