Function Theory On Planar Domains
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| Author | : Stephen D. Fisher |
| Publisher | : Courier Corporation |
| Total Pages | : 292 |
| Release | : 2007-02-27 |
| Genre | : Mathematics |
| ISBN | : 0486457680 |
A high-level treatment of complex analysis, this text focuses on function theory on a finitely connected planar domain. Clear and complete, it emphasizes domains bounded by a finite number of disjoint analytic simple closed curves. The first chapter and parts of Chapters 2 and 3 offer background material, all of it classical and important in its own right. The remainder of the text presents results in complex analysis from the far, middle, and recent past, all selected for their interest and merit as substantive mathematics. Suitable for upper-level undergraduates and graduate students, this text is accessible to anyone with a background in complex and functional analysis. Author Stephen D. Fisher, a professor of mathematics at Northwestern University, elaborates upon and extends results with a set of exercises at the end of each chapter.
| Author | : Stephen D. Fisher |
| Publisher | : Courier Corporation |
| Total Pages | : 292 |
| Release | : 2014-06-10 |
| Genre | : Mathematics |
| ISBN | : 0486151107 |
A high-level treatment of complex analysis, this text focuses on function theory on a finitely connected planar domain. Clear and complete, it emphasizes domains bounded by a finite number of disjoint analytic simple closed curves. The first chapter and parts of Chapters 2 and 3 offer background material, all of it classical and important in its own right. The remainder of the text presents results in complex analysis from the far, middle, and recent past, all selected for their interest and merit as substantive mathematics. Suitable for upper-level undergraduates and graduate students, this text is accessible to anyone with a background in complex and functional analysis. Author Stephen D. Fisher, a professor of mathematics at Northwestern University, elaborates upon and extends results with a set of exercises at the end of each chapter.
| Author | : Stephen D. Fisher |
| Publisher | : |
| Total Pages | : 285 |
| Release | : |
| Genre | : |
| ISBN | : 9780783735184 |
| Author | : Vinh-Thy Minh Tran |
| Publisher | : |
| Total Pages | : |
| Release | : 1998 |
| Genre | : |
| ISBN | : |
We generalize to finitely connected planar domains some classical results concerning composition operators and Toeplitz operators on the Hardy space and Bergman space of the unit disc. In particular, we study how operator-theoretic issues such as compactness and membership in Schattan classes are connected to function-theoretic issues such a value distribution, angular derivatives, and average growth near the boundary. In the process, we also obtain some boundary estimates involving the decay of the Green's function and the growth of certain reproducing kernels.
| Author | : Björn Gustafsson |
| Publisher | : Springer |
| Total Pages | : 152 |
| Release | : 2017-09-29 |
| Genre | : Mathematics |
| ISBN | : 3319658107 |
This book exploits the classification of a class of linear bounded operators with rank-one self-commutators in terms of their spectral parameter, known as the principal function. The resulting dictionary between two dimensional planar shapes with a degree of shade and Hilbert space operators turns out to be illuminating and beneficial for both sides. An exponential transform, essentially a Riesz potential at critical exponent, is at the heart of this novel framework; its best rational approximants unveil a new class of complex orthogonal polynomials whose asymptotic distribution of zeros is thoroughly studied in the text. Connections with areas of potential theory, approximation theory in the complex domain and fluid mechanics are established. The text is addressed, with specific aims, at experts and beginners in a wide range of areas of current interest: potential theory, numerical linear algebra, operator theory, inverse problems, image and signal processing, approximation theory, mathematical physics.
| Author | : Steven G. Krantz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 311 |
| Release | : 2007-09-19 |
| Genre | : Mathematics |
| ISBN | : 0817644407 |
* Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research * Methodically designed with individual chapters containing a rich collection of exercises, examples, and illustrations
| Author | : Peter Ebenfelt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 298 |
| Release | : 2006-03-10 |
| Genre | : Mathematics |
| ISBN | : 3764373164 |
Quadrature domains were singled out about 30 years ago by D. Aharonov and H.S. Shapiro in connection with an extremal problem in function theory. Since then, a series of coincidental discoveries put this class of planar domains at the center of crossroads of several quite independent mathematical theories, e.g., potential theory, Riemann surfaces, inverse problems, holomorphic partial differential equations, fluid mechanics, operator theory. The volume is devoted to recent advances in the theory of quadrature domains, illustrating well the multi-facet aspects of their nature. The book contains a large collection of open problems pertaining to the general theme of quadrature domains.
| Author | : William A. Veech |
| Publisher | : Courier Corporation |
| Total Pages | : 257 |
| Release | : 2014-08-04 |
| Genre | : Mathematics |
| ISBN | : 048615193X |
A clear, self-contained treatment of important areas in complex analysis, this text is geared toward upper-level undergraduates and graduate students. The material is largely classical, with particular emphasis on the geometry of complex mappings. Author William A. Veech, the Edgar Odell Lovett Professor of Mathematics at Rice University, presents the Riemann mapping theorem as a special case of an existence theorem for universal covering surfaces. His focus on the geometry of complex mappings makes frequent use of Schwarz's lemma. He constructs the universal covering surface of an arbitrary planar region and employs the modular function to develop the theorems of Landau, Schottky, Montel, and Picard as consequences of the existence of certain coverings. Concluding chapters explore Hadamard product theorem and prime number theorem.
| Author | : Alexander A. Borichev |
| Publisher | : Birkhäuser |
| Total Pages | : 536 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 3034883625 |
This book is devoted to some topical problems and applications of operator theory and its interplay with modern complex analysis. It consists of 20 selected survey papers that represent updated (mainly plenary) addresses to the IWOTA 2000 conference held at Bordeaux from June 13 to 16, 2000. The main subjects of the volume include: - spectral analysis of periodic differential operators and delay equations, stabilizing controllers, Fourier multipliers; - multivariable operator theory, model theory, commutant lifting theorems, coisometric realizations; - Hankel operators and forms; - operator algebras; - the Bellman function approach in singular integrals and harmonic analysis, singular integral operators and integral representations; - approximation in holomorphic spaces. These subjects are unified by the common "operator theoretic approach" and the systematic use of modern function theory techniques.
| Author | : Vladimir G Maz'ya |
| Publisher | : World Scientific |
| Total Pages | : 502 |
| Release | : 1998-01-15 |
| Genre | : Mathematics |
| ISBN | : 9814498564 |
The spaces of functions with derivatives in Lp, called the Sobolev spaces, play an important role in modern analysis. During the last decades, these spaces have been intensively studied and by now many problems associated with them have been solved. However, the theory of these function classes for domains with nonsmooth boundaries is still in an unsatisfactory state.In this book, which partially fills this gap, certain aspects of the theory of Sobolev spaces for domains with singularities are studied. We mainly focus on the so-called imbedding theorems, extension theorems and trace theorems that have numerous applications to partial differential equations. Some of such applications are given.Much attention is also paid to counter examples showing, in particular, the difference between Sobolev spaces of the first and higher orders. A considerable part of the monograph is devoted to Sobolev classes for parameter dependent domains and domains with cusps, which are the simplest non-Lipschitz domains frequently used in applications.This book will be interesting not only to specialists in analysis but also to postgraduate students.
