Series: Contemporary Mathematicians
2013, XX, 510 p. 1 illus.
Hardcover
ISBN 978-1-4614-7948-2
Due: July 31, 2013
Presents a major portion of the life work of M.M. Schiffer
Serves as an excellent source for researchers and students in the calculus of variations looking for original articles
Contains commentary and annotation to make the work more accessible
M. M. Schiffer, the dominant figure in geometric function theory in the second half of the twentieth century, was a mathematician of exceptional breadth, whose work ranged over such areas as univalent functions, conformal mapping, Riemann surfaces, partial differential equations, potential theory, fluid dynamics, and the theory of relativity. He is best remembered for the powerful variational methods he developed and applied to extremal problems in a wide variety of scientific fields.
Spanning seven decades, the papers collected in these two volumes represent some of Schiffer's most enduring innovations. Expert commentaries provide valuable background and survey subsequent developments. Also included are a complete bibliography and several appreciations of Schiffer's influence by collaborators and other admirers.
Part 4: Reprints.- The Fredholm eigen values of plane domains.- Fredholm eigen values of multiply-connected domains.- Fredholm eigenvalues and conformal mapping.- Fredholm eigenvalues and Grunsky matrices.- Commentary by Reiner KNuhnau.- (with G. PLolya) Sur la repr'esentation conforme de lfextLerieur dfune courbe fermLee convexe.- Commentary by Peter Duren.- Extremum problems and variational methods in conformal mapping.- Commentary by Peter Duren.- (with Z. CharzyLnski) A new proof of the Bieberbach conjecture for the fourth Coefficient.- Commentary by Peter Duren.- (with P. L. Duren) A variational method for functions schlicht in an annulus.- Commentary by Peter Duren.- (with B. Epstein) On the mean-value property of harmonic functions.- Commentary by Lawrence Zalcman.- (with N. S. Hawley) Half-order differentials on Riemann surfaces.- Commentary by John Fay.- (with P. R. Garabedian) The local maximum theorem for the coefficients of univalent functions.- Commentary by Peter Duren.- Some distortion theorems in the theory of conformal mapping.- Commentary by Peter Duren.- (with G. Schober) An extremal problem for the Fredholm eigenvalues.- (with G. Schober) A remark on the paper gAn extremal problem for the Fredholm eigenvaluesh.- (with G. Schober) A variational method for general families of quasiconformal mappings.- Commentary by Reiner Kuhnau.- (with J. Hersch and L. E. Payne) Some inequalities for Stekloff eigenvalues.- Commentary by Bodo Dittmar.- (with J. A. Hummel) Variational methods for Bieberbach-Eilenberg functions and for pairs.- Commentary by Dov Aharonov.- (with J. A. Hummel and B. Pinchuk) Bounded univalent functions which cover a fixed disc.- Commentary by Bernard Pinchuk.- (with G. Schober) The dielectric Greenfs function and quasiconformal mapping.- Commentary by Brad Osgood.- (with A. Chang and G. Schober) On the second variation for univalent functions.- Commentary by Peter Duren.- (with D. Aharonov and L. Zalcman) Potato kugel.- Commentary by Lawrence Zalcman.- (with P. L. Duren and Y. J. Leung) Support points with maximum radial angle.- Commentary by Peter Duren.- (with P. L. Duren) Univalent functions which map onto regions of given transfinite diameter.- Commentary by Peter Duren.- (with P. L. Duren) Robin functions and distortion of capacity under conformal mapping.- Commentary by Peter Duren.- Issai Schur: Some personal reminiscences.-Commentary by Lawrence Zalcman.
Series: Graduate Texts in Mathematics, Vol. 268
2013, XVI, 342 p. 7 illus.
Hardcover
ISBN 978-1-4614-7923-9
Due: August 16, 2013
Several topics are presented for the first time in book form
Textbook for graduate students that will also benefit seasoned researchers in mathematics
Includes illustrative examples and carefully chosen exercises
Discusses applications to function theory, geometry, partial differential equations, and interpretations in terms of functional analysis
This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculation, invariance properties, boundary asymptotics, and asymptotic expansion of the Bergman kernel and metric. Moreover, it presents a unique compendium of results with applications to function theory, geometry, partial differential equations, and interpretations in the language of functional analysis, with emphasis on the several complex variables context. Several of these topics appear here for the first time in book form. Each chapter includes illustrative examples and a collection of exercises which will be of interest to both graduate students and experienced mathematicians.
Graduate students who have taken courses in complex variables
and have a basic background in real and functional analysis will find this textbook appealing. Applicable courses for either main or supplementary usage include those in complex variables, several complex variables, complex differential geometry, and partial differential equations. Researchers in complex analysis, harmonic analysis, PDEs, and complex differential geometry will also benefit from the thorough treatment of the many exciting aspects of Bergman's theory.
Preface.- 1. Introductory Ideas.- 2. The Bergman Metric.- 3. Geometric and Analytic Ideas.- 4. Partial Differential Equations.- 5. Further Geometric Explorations.- 6. Additional Analytic Topics.- 7. Curvature of the Bergman Metric.- 8. Concluding Remarks.- Table of Notation.- Bibliography.- Index.
Series: Lecture Notes in Mathematics, Vol. 2083
2013, X, 211 p. 42 illus.
Softcover
ISBN 978-3-642-38741-8
Due: June 30, 2013
.Chapters cover leading-edge aspects of the theory of monomial ideals written by top researchers in their fields
Includes computer tutorials that highlight the computational aspects of the area
Carefully written introductions to topics of current research interest
This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jurgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Alvarez Montaner. The chapters, written by top experts, include computer tutorials that emphasize the computational aspects of the respective areas. Monomial ideals and algebras are, in a sense, among the simplest structures in commutative algebra and the main objects of combinatorial commutative algebra. Also, they are of major importance for at least three reasons. Firstly, Grobner basis theory allows us to treat certain problems on general polynomial ideals by means of monomial ideals. Secondly, the combinatorial structure of monomial ideals connects them to other combinatorial structures and allows us to solve problems on both sides of this correspondence using the techniques of each of the respective areas. And thirdly, the combinatorial nature of monomial ideals also makes them particularly well suited to the development of algorithms to work with them and then generate algorithms for more general structures.
A survey on Stanley depth.- Stanley decompositions using CoCoA.- A beginnerfs guide to edge and cover ideals.- Edge ideals using Macaulay2.- Local cohomology modules supported on monomial ideals.- Local Cohomology using Macaulay2.
Series: Lecture Notes in Mathematics, Vol. 2084
2013, Approx. 625 p.
Softcover
ISBN 978-3-319-00824-0
Due: August 31, 2013
The arguments for the main results are detailed and self-contained
At least one typical and easily explicable example is given for each important notion further clarifying the relationship between the known and the present notionsDetailed references for the content of each chapter are given. Also, well-known related results and some unsolved problems, which will be of interest to the reader, are presented, which might be interesting to the reader
The present book offers an essential but accessible introduction to the discoveries first made in the 1990s that the doubling condition is superfluous for most results for function spaces and the boundedness of operators. It shows the methods behind these discoveries, their consequences and some of their applications. It also provides detailed and comprehensive arguments, many typical and easy-to-follow examples, and interesting unsolved problems.
The theory of the Hardy space is a fundamental tool for Fourier analysis, with applications for and connections to complex analysis, partial differential equations, functional analysis and geometrical analysis. It also extends to settings where the doubling condition of the underlying measures may fail.
Preliminaries.- Approximations of the Identity.- The Hardy Space H1(Ê).- The Local Atomic Hardy Space h1(Ê).- Boundedness of Operators over (RD, Ê).- Littlewood-Paley Operators and Maximal Operators Related to Approximations of the Identity.- The Hardy Space H1 (Ô, Ò)and Its Dual Space RBMO (Ô, Ò).- Boundedness of Operators over((Ô, Ò).- Bibliography.- Index.- Abstract.
Series: Lecture Notes in Mathematics, Vol. 2085
2013, Approx. 180 p. 9 illus. in color.
Softcover I
ISBN 978-3-319-00827-1
Due: August 31, 2013
The comprehensive presentation serves as an excellent basis for a Master's course on stochastic partial differential equations(SPDEs) with Levy noise
The showcase character of this study provides particular insight into the methods developed and stimulates future researchAn additional chapter connects the mathematical results to its climatological motivation
This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval. It has two stable points whose domains of attraction meet in a separating manifold with several saddle points. Extending a method developed by Imkeller and Pavlyukevich it proves that in contrast to a Gaussian perturbation, the expected exit and transition times between the domains of attraction depend polynomially on the noise intensity in the small intensity limit. Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamic behavior of a finite-state Markov chain switching between the stable states.
Introduction.- The fine dynamics of the Chafee- Infante equation.- The stochastic Chafee- Infante equation.- The small deviation of the small noise solution.- Asymptotic exit times.- Asymptotic transition times.- Localization and metastability.- The source of stochastic models in conceptual climate dynamics.