Weighted Bergman Spaces Induced by Rapidly Increasing Weights
Author: José Ángel Peláez
Publisher:
Published: 2014-10-03
Total Pages: 124
ISBN-13: 9781470414276
DOWNLOAD EBOOK →January 2014, volume 227, number 1066 (second of 4 numbers).
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Weighted Bergman Spaces Induced by Rapidly Increasing Weights
Author: Jose Angel Pelaez
Publisher: American Mathematical Soc.
Published: 2014-01-08
Total Pages: 136
ISBN-13: 0821888021
DOWNLOAD EBOOK →This monograph is devoted to the study of the weighted Bergman space $A^p_\omega$ of the unit disc $\mathbb{D}$ that is induced by a radial continuous weight $\omega$ satisfying $\lim_{r\to 1^-}\frac{\int_r^1\omega(s)\,ds}{\omega(r)(1-r)}=\infty.$ Every such $A^p_\omega$ lies between the Hardy space $H^p$ and every classical weighted Bergman space $A^p_\alpha$. Even if it is well known that $H^p$ is the limit of $A^p_\alpha$, as $\alpha\to-1$, in many respects, it is shown that $A^p_\omega$ lies ``closer'' to $H^p$ than any $A^p_\alpha$, and that several finer function-theoretic properties of $A^p_\alpha$ do not carry over to $A^p_\omega$.
Function Classes on the Unit Disc
Author: Miroslav Pavlović
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2019-08-19
Total Pages: 574
ISBN-13: 3110630850
DOWNLOAD EBOOK →This revised and extended edition of a well-established monograph in function theory contains a study on various function classes on the disc, a number of new results and new or easy proofs of old but interesting theorems (for example, the Fefferman–Stein theorem on subharmonic behavior or the theorem on conjugate functions in Bergman spaces) and a full discussion on g-functions.
Advanced Courses Of Mathematical Analysis Vi - Proceedings Of The Sixth International School
Author: Francisco Javier Martin-reyes
Publisher: World Scientific
Published: 2016-10-27
Total Pages: 248
ISBN-13: 9813147652
DOWNLOAD EBOOK →This volume contains short courses and recent papers by several specialists in different fields of Mathematical Analysis. It offers a wide perspective of the current state of research, and new trends, in areas related to Geometric Analysis, Harmonic Analysis, Complex Analysis, Functional Analysis and History of Mathematics. The contributions are presented with a remarkable expository nature and this makes the discussed topics accessible to a more general audience.
Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces
Author: David Dos Santos Ferreira
Publisher: American Mathematical Soc.
Published: 2014-04-07
Total Pages: 86
ISBN-13: 0821891197
DOWNLOAD EBOOK →The authors investigate the global continuity on spaces with of Fourier integral operators with smooth and rough amplitudes and/or phase functions subject to certain necessary non-degeneracy conditions. In this context they prove the optimal global boundedness result for Fourier integral operators with non-degenerate phase functions and the most general smooth Hörmander class amplitudes i.e. those in with . They also prove the very first results concerning the continuity of smooth and rough Fourier integral operators on weighted spaces, with and (i.e. the Muckenhoupt weights) for operators with rough and smooth amplitudes and phase functions satisfying a suitable rank condition.
A Homology Theory for Smale Spaces
Author: Ian F. Putnam
Publisher: American Mathematical Soc.
Published: 2014-09-29
Total Pages: 136
ISBN-13: 1470409097
DOWNLOAD EBOOK →The author develops a homology theory for Smale spaces, which include the basics sets for an Axiom A diffeomorphism. It is based on two ingredients. The first is an improved version of Bowen's result that every such system is the image of a shift of finite type under a finite-to-one factor map. The second is Krieger's dimension group invariant for shifts of finite type. He proves a Lefschetz formula which relates the number of periodic points of the system for a given period to trace data from the action of the dynamics on the homology groups. The existence of such a theory was proposed by Bowen in the 1970s.
Blaschke Products and Their Applications
Author: Javad Mashreghi
Publisher: Springer Science & Business Media
Published: 2012-10-05
Total Pages: 324
ISBN-13: 1461453402
DOWNLOAD EBOOK →Blaschke Products and Their Applications presents a collection of survey articles that examine Blaschke products and several of its applications to fields such as approximation theory, differential equations, dynamical systems, harmonic analysis, to name a few. Additionally, this volume illustrates the historical roots of Blaschke products and highlights key research on this topic. For nearly a century, Blaschke products have been researched. Their boundary behaviour, the asymptomatic growth of various integral means and their derivatives, their applications within several branches of mathematics, and their membership in different function spaces and their dynamics, are a few examples of where Blaschke products have shown to be important. The contributions written by experts from various fields of mathematical research will engage graduate students and researches alike, bringing the reader to the forefront of research in the topic. The readers will also discover the various open problems, enabling them to better pursue their own research.
Special Values of Automorphic Cohomology Classes
Author: Mark Green
Publisher: American Mathematical Soc.
Published: 2014-08-12
Total Pages: 158
ISBN-13: 0821898574
DOWNLOAD EBOOK →The authors study the complex geometry and coherent cohomology of nonclassical Mumford-Tate domains and their quotients by discrete groups. Their focus throughout is on the domains which occur as open -orbits in the flag varieties for and , regarded as classifying spaces for Hodge structures of weight three. In the context provided by these basic examples, the authors formulate and illustrate the general method by which correspondence spaces give rise to Penrose transforms between the cohomologies of distinct such orbits with coefficients in homogeneous line bundles.
Transfer of Siegel Cusp Forms of Degree 2
Author: Ameya Pitale
Publisher: American Mathematical Soc.
Published: 2014-09-29
Total Pages: 120
ISBN-13: 0821898566
DOWNLOAD EBOOK →Let be the automorphic representation of generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and be an arbitrary cuspidal, automorphic representation of . Using Furusawa's integral representation for combined with a pullback formula involving the unitary group , the authors prove that the -functions are "nice". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations have a functorial lifting to a cuspidal representation of . Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of to a cuspidal representation of . As an application, the authors obtain analytic properties of various -functions related to full level Siegel cusp forms. They also obtain special value results for and
Combinatorial Floer Homology
Author: Vin de Silva
Publisher: American Mathematical Soc.
Published: 2014-06-05
Total Pages: 126
ISBN-13: 0821898868
DOWNLOAD EBOOK →The authors define combinatorial Floer homology of a transverse pair of noncontractible nonisotopic embedded loops in an oriented -manifold without boundary, prove that it is invariant under isotopy, and prove that it is isomorphic to the original Lagrangian Floer homology. Their proof uses a formula for the Viterbo-Maslov index for a smooth lune in a -manifold.
