Carleman's Formulas in Complex Analysis
Theory and Applications
Published on 31. January 1993
Book
Hardback
XX, 299 pages
978-0-7923-2121-7 (ISBN)
Description
Integral representations of holomorphic functions play an important part in the classical theory of functions of one complex variable and in multidimensional com plex analysis (in the later case, alongside with integration over the whole boundary aD of a domain D we frequently encounter integration over the Shilov boundary 5 = S(D)). They solve the classical problem of recovering at the points of a do main D a holomorphic function that is sufficiently well-behaved when approaching the boundary aD, from its values on aD or on S. Alongside with this classical problem, it is possible and natural to consider the following one: to recover the holomorphic function in D from its values on some set MeaD not containing S. Of course, M is to be a set of uniqueness for the class of holomorphic functions under consideration (for example, for the functions continuous in D or belonging to the Hardy class HP(D), p ~ 1).
More details
Series
Edition
1993 ed.
Language
English
Place of publication
Dordrecht
Netherlands
Target group
Professional and scholarly
Research
Illustrations
XX, 299 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 22 mm
Weight
647 gr
ISBN-13
978-0-7923-2121-7 (9780792321217)
DOI
10.1007/978-94-011-1596-4
Schweitzer Classification
Other editions
Additional editions
Book
10/2012
Springer
€53.49
Shipment within 15-20 days
Content
I. Carleman Formulas in the Theory of Functions of One Complex Variable and their Generalizations.- I. One-Dimensional Carleman Formulas.- II. Generalization of One-Dimensional Carleman Formulas.- II. Carleman Formulas in Multidimensional Complex Analysis.- III. Integral Representations of Holomorphic Functions of Several Complex Variables and Logarithmic Residues.- IV. Multidimensional Analog of Carleman Formulas with Integration over Boundary Sets of Maximal Dimension.- V. Multidimensional Carleman Formulas for Sets of Smaller Dimension.- VI. Carleman Formulas in Homogeneous Domains.- III. First Applications.- VII. Applications in Complex Analysis.- VIII. Applications in Physics and Signal Processing.- IX. Computing Experiment.- IV. Supplement to the English Edition.- X. Criteria for Analytic Continuation. Harmonic Extension.- XI. Carleman Formulas and Related Problems.- Notes.- Index of Proper Names.- Index of Symbols.