The Theory of H(b) Spaces: Volume 1
The Theory of H(b) Spaces: Volume 1

Author: Emmanuel Fricain

Publisher: Cambridge University Press

Published: 2016-05-26

Total Pages: 703

ISBN-13: 1316060918

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An H(b) space is defined as a collection of analytic functions which are in the image of an operator. The theory of H(b) spaces bridges two classical subjects: complex analysis and operator theory, which makes it both appealing and demanding. The first volume of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators, and Clark measures. The second volume focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.

The Theory of H(b) Spaces: Volume 2
The Theory of H(b) Spaces: Volume 2

Author: Emmanuel Fricain

Publisher: Cambridge University Press

Published: 2016-10-20

Total Pages: 641

ISBN-13: 1316351920

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An H(b) space is defined as a collection of analytic functions that are in the image of an operator. The theory of H(b) spaces bridges two classical subjects, complex analysis and operator theory, which makes it both appealing and demanding. Volume 1 of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators and Clark measures. Volume 2 focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.

Analytic Function Theory, Volume I
Analytic Function Theory, Volume I

Author: Einar Hille

Publisher: American Mathematical Soc.

Published: 2012-04-11

Total Pages: 322

ISBN-13: 082187568X

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Second Edition. This famous work is a textbook that emphasizes the conceptual and historical continuity of analytic function theory. The second volume broadens from a textbook to a textbook-treatise, covering the "canonical" topics (including elliptic functions, entire and meromorphic functions, as well as conformal mapping, etc.) and other topics nearer the expanding frontier of analytic function theory. In the latter category are the chapters on majorization and on functions holomorphic in a half-plane.

Homeostatic Blood States Theory
Homeostatic Blood States Theory

Author: Audrius Andrijauskas

Publisher: Universal-Publishers

Published: 2008-01-31

Total Pages: 272

ISBN-13: 1599426536

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Intravenous fluid and blood component resuscitation is an integral part of modern medicine practice in a variety of medical fields. However, these therapies are usually led by rigid and very approximate guidelines. The purpose of creating the Homeostatic blood states theory was to develop more accurate guidelines. On the basis of the new theory the following results have been reached: 1. The physiological-mathematical model explaining blood volume homeostasis has been created; 2. Nomograms for infusion therapy measures, blood loss evaluation and calculating red blood cell transfusion amount were proposed; 3. Nomograms were built on the background of interfering relationship of blood hematocrit and hemoglobin concentration; 4. New guidelines for infusion therapy, blood loss evaluation and calculating transfusion amount for proper hematocrit increase were proposed; 5. New method for early verification of occult bleeding has been suggested. Three major homeostatic blood states were described: (1) target state, (2) state of maximal isoosmotic plasma dilution and (3) dehydration. Target states maintain optimal red cell mass and blood volume correlation. Other two maintain critical plasma hydration origin deviations from target state. Three new nomograms enable planning and evaluation of infusion therapy and red cell mass transfusion, quantitate evaluation of blood loss and early detection of occult bleeding based on the dynamics of blood hematocrit and hemoglobin concentration.

Functional Analysis, Approximation Theory And Numerical Analysis
Functional Analysis, Approximation Theory And Numerical Analysis

Author: John Michael Rassias

Publisher: World Scientific

Published: 1994-06-09

Total Pages: 340

ISBN-13: 9814506052

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This book consists of papers written by outstanding mathematicians. It deals with both theoretical and applied aspects of the mathematical contributions of BANACH, ULAM, and OSTROWSKI, which broaden the horizons of Functional Analysis, Approximation Theory, and Numerical Analysis in accordance with contemporary mathematical standards.

Photons In Fock Space And Beyond (In 3 Volumes)
Photons In Fock Space And Beyond (In 3 Volumes)

Author: Reinhard Honegger

Publisher: World Scientific

Published: 2015-04-22

Total Pages: 2353

ISBN-13: 9814618853

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The three-volume major reference “Photons in Fock Space and Beyond” undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum optical notions are generalized beyond Fock representations where the richness of an infinite dimensional quantum field system, with its mathematical difficulties and theoretical possibilities, is fully taken into account. It aims at a microscopic formulation of a mesoscopic model class which covers in principle all stages of the generation and propagation of light within a unified and well-defined conceptual frame.The dynamics of the interacting systems is founded — according to original works of the authors — on convergent perturbation series and describes the developments of the quantized microscopic as well as the classical collective degrees of freedom at the same time. The achieved theoretical unification fits especially to laser and microwave applications inheriting objective information over quantum noise.A special advancement is the incorporation of arbitrary multiply connected cavities where ideal conductor boundary conditions are imposed. From there arises a new category of classical and quantized field parts, apparently not treated in Quantum Electrodynamics before. In combination with gauge theory, the additional “cohomological fields” explain topological quantum effects in superconductivity. Further applications are to be expected for optoelectronic and optomechanical systems.

Mathematical Methods in Quantum Mechanics
Mathematical Methods in Quantum Mechanics

Author: Gerald Teschl

Publisher: American Mathematical Soc.

Published: 2009

Total Pages: 322

ISBN-13: 0821846604

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Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. It is well suited for self-study and includes numerous exercises (many with hints).

Physics Of Reality, The: Space, Time, Matter, Cosmos - Proceedings Of The 8th Symposium Honoring Mathematical Physicist Jean-pierre Vigier
Physics Of Reality, The: Space, Time, Matter, Cosmos - Proceedings Of The 8th Symposium Honoring Mathematical Physicist Jean-pierre Vigier

Author: Richard L Amoroso

Publisher: World Scientific

Published: 2013-09-18

Total Pages: 553

ISBN-13: 9814504793

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A truly Galilean-class volume, this book introduces a new method in theory formation, completing the tools of epistemology. It covers a broad spectrum of theoretical and mathematical physics by researchers from over 20 nations from four continents. Like Vigier himself, the Vigier symposia are noted for addressing avant-garde, cutting-edge topics in contemporary physics. Among the six proceedings honoring J.-P. Vigier, this is perhaps the most exciting one as several important breakthroughs are introduced for the first time. The most interesting breakthrough in view of the recent NIST experimental violations of QED is a continuation of the pioneering work by Vigier on tight bound states in hydrogen. The new experimental protocol described not only promises empirical proof of large-scale extra dimensions in conjunction with avenues for testing string theory, but also implies the birth of the field of unified field mechanics, ushering in a new age of discovery. Work on quantum computing redefines the qubit in a manner that the uncertainty principle may be routinely violated. Other breakthroughs occur in the utility of quaternion algebra in extending our understanding of the nature of the fermionic singularity or point particle. There are several other discoveries of equal magnitude, making this volume a must-have acquisition for the library of any serious forward-looking researchers.

The Theory of H(b) Spaces
The Theory of H(b) Spaces

Author: Emmanuel Fricain

Publisher: Cambridge University Press

Published: 2016-05-26

Total Pages: 703

ISBN-13: 1107027772

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This is volume 1 of a 2 volume set.