Title | Analytic Extension Formulas and their Applications [electronic resource] / edited by Saburou Saitoh, Nakao Hayashi, Masahiro Yamamoto |
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Imprint | Boston, MA : Springer US : Imprint: Springer, 2001 |

Connect to | http://dx.doi.org/10.1007/978-1-4757-3298-6 |

Descript | VIII, 288 p. online resource |

SUMMARY

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

1. Extending holomorphic functions from subvarieties -- 2. Representations of analytic functions on typical domains in terms of local values and truncation error estimates -- 3. Uniqueness in determining damping coefficients in hyperbolic equations -- 4. Analytic continuation of Cauchy and exponential transforms -- 5. Analytic function spaces and their applications to nonlinear evolution equations -- 6. A sampling principle associated with Saitohโ{128}{153}s fundamental theory of linear transformations -- 7. The enclosure method and its applications -- 8. On analytic properties of a multiple L-function -- 9. Multi-dimensional inverse scattering theory -- 10. Holomorphic spaces related to orthogonal polynomials and analytic continuation of functions -- 11. Extension and division on complex manifolds -- 12. Analytic extension formulas, integral transforms and reproducing kernels -- 13. Analytic continuation beyond the ideal boundary -- 14. Justification of a formal derivation of the Euler-Maclaurin summation formula -- 15. Extension of Lรถwner-Heinz inequality via analytic continuation -- 16. The Calogero-Moser model, the Calogero model and analytic extension

Mathematics
Functions of complex variables
Integral transforms
Operational calculus
Partial differential equations
Potential theory (Mathematics)
Mathematics
Functions of a Complex Variable
Several Complex Variables and Analytic Spaces
Partial Differential Equations
Integral Transforms Operational Calculus
Potential Theory