Spectral Theory of Ordinary Differential Operators


Author: Joachim Weidmann
Publisher: Springer
ISBN: 3540479120
Category: Mathematics
Page: 304
View: 7500
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These notes will be useful and of interest to mathematicians and physicists active in research as well as for students with some knowledge of the abstract theory of operators in Hilbert spaces. They give a complete spectral theory for ordinary differential expressions of arbitrary order n operating on -valued functions existence and construction of self-adjoint realizations via boundary conditions, determination and study of general properties of the resolvent, spectral representation and spectral resolution. Special attention is paid to the question of separated boundary conditions, spectral multiplicity and absolutely continuous spectrum. For the case nm=2 (Sturm-Liouville operators and Dirac systems) the classical theory of Weyl-Titchmarch is included. Oscillation theory for Sturm-Liouville operators and Dirac systems is developed and applied to the study of the essential and absolutely continuous spectrum. The results are illustrated by the explicit solution of a number of particular problems including the spectral theory one partical Schrödinger and Dirac operators with spherically symmetric potentials. The methods of proof are functionally analytic wherever possible.

Spectral Theory of Differential Operators


Author: I.W. Knowles,R.T. Lewis
Publisher: Elsevier
ISBN: 9780080871660
Category: Mathematics
Page: 383
View: 2274
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Spectral Theory of Differential Operators

Spectral Theory and Mathematical Physics: Ergodic Schrödinger operators, singular spectrum, orthogonal polynomials, and inverse spectral theory


Author: Barry Simon
Publisher: American Mathematical Soc.
ISBN: 0821842498
Category: Mathematics
Page: 948
View: 4055
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This Festschrift had its origins in a conference called SimonFest held at Caltech, March 27-31, 2006, to honor Barry Simon's 60th birthday. It is not a proceedings volume in the usual sense since the emphasis of the majority of the contributions is on reviews of the state of the art of certain fields, with particular focus on recent developments and open problems. The bulk of the articles in this Festschrift are of this survey form, and a few review Simon's contributions to a particular area. Part 1 contains surveys in the areas of Quantum Field Theory, Statistical Mechanics, Nonrelativistic Two-Body and $N$-Body Quantum Systems, Resonances, Quantum Mechanics with Electric and Magnetic Fields, and the Semiclassical Limit. Part 2 contains surveys in the areas of Random and Ergodic Schrodinger Operators, Singular Continuous Spectrum, Orthogonal Polynomials, and Inverse Spectral Theory. In several cases, this collection of surveys portrays both the history of a subject and its current state of the art. A substantial part of the contributions to this Festschrift are survey articles on the state of the art of certain areas with special emphasis on open problems. This will benefit graduate students as well as researchers who want to get a quick, yet comprehensive introduction into an area covered in this volume.

Degenerate Differential Equations in Banach Spaces


Author: Angelo Favini,Atsushi Yagi
Publisher: CRC Press
ISBN: 9780824716776
Category: Mathematics
Page: 336
View: 2019
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This work presents a detailed study of linear abstract degenerate differential equations, using both the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. The authors describe the recent and original results on PDEs and algebraic-differential equations, and establishes the analyzability of the semigroup generated by some degenerate parabolic operators in spaces of continuous functions.

Spectral Theory and Differential Operators


Author: David Edmunds,Des Evans
Publisher: Oxford University Press
ISBN: 0198812051
Category: Mathematics
Page: 624
View: 5847
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This book is an updated version of the classic 1987 monograph "Spectral Theory and Differential Operators".The original book was a cutting edge account of the theory of bounded and closed linear operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. It is accessible to a graduate student as well as meeting the needs of seasoned researchers in mathematics and mathematical physics. This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.

Spectral Theory and Asymptotics of Differential Equations

Proceedings of the Scheveningen Conference on Differential Equations, the Netherlands
Author: N.A
Publisher: Elsevier
ISBN: 9780080871240
Category: Mathematics
Page: 209
View: 9667
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Spectral Theory and Asymptotics of Differential Equations

Lecture Notes in Mathematics


Author: Albrecht Dold,Hans Volkmer
Publisher: Springer Verlag
ISBN: N.A
Category: Matrices
Page: 157
View: 7217
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Spectral theory of ordinary differential operators


Author: Erich Müller-Pfeiffer
Publisher: N.A
ISBN: 9780853121893
Category: Mathematics
Page: 246
View: 7716
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Periodic Differential Operators


Author: B. Malcolm Brown,Michael S.P. Eastham,Karl Michael Schmidt
Publisher: Springer Science & Business Media
ISBN: 3034805284
Category: Mathematics
Page: 220
View: 3465
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Periodic differential operators have a rich mathematical theory as well as important physical applications. They have been the subject of intensive development for over a century and remain a fertile research area. This book lays out the theoretical foundations and then moves on to give a coherent account of more recent results, relating in particular to the eigenvalue and spectral theory of the Hill and Dirac equations. The book will be valuable to advanced students and academics both for general reference and as an introduction to active research topics.

Recent Developments in Operator Theory and Its Applications

International Conference in Winnipeg, October 2–6, 1994
Author: I. Gohberg,Peter Lancaster,P.N. Shivakumar
Publisher: Springer Science & Business Media
ISBN: 9783764354138
Category: Mathematics
Page: 436
View: 5278
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The papers selected for publication here, many of them written by leaders in the field, bring readers up to date on recent achievements in modern operator theory and applications. The book’s subject matter is of practical use to a wide audience in mathematical and engineering sciences.

Featured Reviews in Mathematical Reviews 1997-1999

With Selected Reviews of Classic Books and Papers from 1940-1969
Author: Donald G. Babbitt,Jane E. Kister
Publisher: American Mathematical Soc.
ISBN: 9780821896709
Category: Mathematics
Page: 541
View: 6880
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This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.

Hyperbolic Partial Differential Equations

Modern Applied Mathematics and Computer Science
Author: Matthew Witten
Publisher: Elsevier
ISBN: 1483151352
Category: Mathematics
Page: 268
View: 2102
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Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic McKendrick equations for age-structured population growth; and logistic models of structured population growth. A number of book reviews are also included. This journal provides an interdisciplinary forum for the presentation of results not included in other particular journals, and thus will be beneficial to those interested in this field of study.

Spectral Theory of Indefinite Krein-Feller Differential Operators


Author: Andreas Fleige
Publisher: Wiley-VCH
ISBN: N.A
Category: Mathematics
Page: 134
View: 9445
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The vibration of a string with a (nondecreasing) mass distribution function m leads to a generalized differential equation of second order, introduced by Krein and by Feller. The author allows also nonmonotonic functions m and hence, gets into the theory of indefinite inner product spaces. Here at the first time a systematic presentation of the generalized differential expression and of J-selfadjoint operator realizations is given. Developing a spectral theory for such Krein-Feller operators, the author derives the most general known criteria for the regularity of the critical point infinity. Then, by specialization, expansion theorems for wide classes of indefinite second order differential and difference operators are obtained.

Spectral Theory and Differential Operators


Author: E. Brian Davies,Edward Brian Davies
Publisher: Cambridge University Press
ISBN: 9780521587105
Category: Mathematics
Page: 182
View: 4073
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In this book, Davies introduces the reader to the theory of partial differential operators, up to the spectral theorem for bounded linear operators on Banach spaces. He also describes the theory of Fourier transforms and distributions as far as is needed to analyze the spectrum of any constant coefficient partial differential operator. He also presents a completely new proof of the spectral theorem for unbounded self-adjoint operators and demonstrates its application to a variety of second order elliptic differential operators. Finally, the book contains a detailed account of the application of variational methods to estimate the eigenvalues of operators with measurable coefficients defined by the use of quadratic form techniques. Illustrated with many examples, it is well-suited to graduate-level work.

Partial Differential Equations II

Qualitative Studies of Linear Equations
Author: Michael E. Taylor
Publisher: Springer Science & Business Media
ISBN: 9781441970527
Category: Mathematics
Page: 614
View: 2355
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This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centred about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion.

Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods, and Theory


Author: Carlos Castillo-Chavez,Sally Blower,Pauline van den Driessche,Denise Kirschner,Abdul-Aziz Yakubu
Publisher: Springer Science & Business Media
ISBN: 9780387953557
Category: Medical
Page: 377
View: 2767
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This IMA Volume in Mathematics and its Applications MATHEMATICAL APPROACHES FOR EMERGING AND REEMERGING INFECTIOUS DISEASES: MODELS, AND THEORY METHODS is based on the proceedings of a successful one week workshop. The pro ceedings of the two-day tutorial which preceded the workshop "Introduction to Epidemiology and Immunology" appears as IMA Volume 125: Math ematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction. The tutorial and the workshop are integral parts of the September 1998 to June 1999 IMA program on "MATHEMATICS IN BI OLOGY. " I would like to thank Carlos Castillo-Chavez (Director of the Math ematical and Theoretical Biology Institute and a member of the Depart ments of Biometrics, Statistics and Theoretical and Applied Mechanics, Cornell University), Sally M. Blower (Biomathematics, UCLA School of Medicine), Pauline van den Driessche (Mathematics and Statistics, Uni versity of Victoria), and Denise Kirschner (Microbiology and Immunology, University of Michigan Medical School) for their superb roles as organizers of the meetings and editors of the proceedings. Carlos Castillo-Chavez, es pecially, made a major contribution by spearheading the editing process. I am also grateful to Kenneth L. Cooke (Mathematics, Pomona College), for being one of the workshop organizers and to Abdul-Aziz Yakubu (Mathe matics, Howard University) for serving as co-editor of the proceedings. I thank Simon A. Levin (Ecology and Evolutionary Biology, Princeton Uni versity) for providing an introduction.

Nonlinear Spectral Theory


Author: Jürgen Appell,Espedito De Pascale,Alfonso Vignoli
Publisher: Walter de Gruyter
ISBN: 3110199262
Category: Mathematics
Page: 419
View: 5555
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In view of the eminent importance of spectral theory of linear operators in many fields of mathematics and physics, it is not surprising that various attempts have been made to define and study spectra also for nonlinear operators. This book provides a comprehensive and self-contained treatment of the theory, methods, and applications of nonlinear spectral theory. The only prerequisite for understanding this book is a modest background in functional analysis and operator theory. It is addressed to non-specialists who want to get an idea of the development of spectral theory for nonlinear operators in the last 30 years, as well as a glimpse of the diversity of the directions in which current research is moving.

Two-parameter eigenvalue problems in ordinary differential equations


Author: M. Faierman
Publisher: Chapman & Hall/CRC
ISBN: N.A
Category: Mathematics
Page: 160
View: 7724
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Mathematical Physics of Quantum Mechanics

Selected and Refereed Lectures from QMath9
Author: Joachim Asch,Alain Joye
Publisher: Springer
ISBN: 3540342737
Category: Science
Page: 462
View: 7341
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This selection of outstanding articles – an outgrowth of the QMath9 meeting for young scientists – covers new techniques and recent results on spectral theory, statistical mechanics, Bose-Einstein condensation, random operators, magnetic Schrödinger operators and more. The book’s pedagogical style makes it a useful introduction to the research literature for postgraduate students. For more expert researchers it will serve as a concise source of modern reference.

Spectral Theory of Differential Operators

M. Sh. Birman 80th Anniversary Collection
Author: T. Suslina
Publisher: American Mathematical Soc.
ISBN: 9780821890776
Category: Mathematics
Page: 299
View: 8996
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