Edited by: W. H. Schikhof, University of Nijmegen, The Netherlands, C. Perez-Garcia, Universidad de Cantabria, Santander, Spain, and A. Escassut, Universite Blaise Pascal, Aubiere, France

Ultrametric Functional Analysis

Expected publication date is April 27, 2003

Description

This volume contains research articles based on lectures given at the Seventh International Conference on p-adic Functional Analysis.

The articles, written by leading international experts, provide a complete overview of the latest contributions in basic functional analysis (Hilbert and Banach spaces, locally convex spaces, orthogonality, inductive limits, spaces of continuous functions, strict topologies, operator theory, automatic continuity, measure and integrations, Banach and topological algebras, summability methods, and ultrametric spaces), analytic functions (meromorphic functions, roots of rational functions, characterization of injective holomorphic functions, and Gelfand transforms in algebras of analytic functions), differential equations, Banach-Hopf algebras, Cauchy theory of Levi-Civita fields, finite differences, weighted means, p-adic dynamical systems, and non-Archimedean probability theory and stochastic processes.

The book is written for graduate students and research mathematicians. It also would make a good reference source for those in related areas, such as classical functional analysis, complex analytic functions, probability theory, dynamical systems, orthomodular spaces, number theory, and representations of p-adic groups.

Contents

J. Aguayo and M. Nova -- Non-archimedean integral operators on the space of continuous functions
J. Araujo -- Isomorphisms with small bound between spaces of p-adic continuous functions
E. Beckenstein and L. Narici -- Automatic continuity of basis separating maps
M. Berz -- Cauchy theory on Levi-Civita fields
A. Boutabaa and A. Escassut -- Uniqueness problems and applications of the ultrametric Nevanlinna theory
B. Diarra -- The Hopf algebra structure of the space of continuous functions on power series over mathbb{F}_q and Carlitz polynomials
N. De Grande-de Kimpe, J. Kakol, and C. Perez-Garcia -- Metrizability of compactoid sets in non-archimedean Hausdorff (LM)-spaces
A. K. Katsaras -- Strict topologies and vector-measures on non-archimedean spaces
A. K. Katsaras and C. G. Petalas -- P-adic spaces with strict topologies as topological algebras
A. Khrennikov and S. Ludkovsky -- Non-archimedean stochastic processes
A. Khrennikov, M. Nilsson, and R. Nyqvist -- The asymptotic number of periodic points of discrete polynomial p-adic dynamical systems
A. N. Kochubei -- Analysis and probability over infinite extensions of a local field, II: A multiplicative theory
A. Kubzdela -- The Hahn-Banach subspaces of Banach spaces with base
A. J. Lemin and V. Lemin -- On metrically universal ultrametric spaces LV_{tau} and LW_{tau}
N. Mainetti -- Gelfand transform and spectral radius formulae for ultrametric Banach algebras
P. N. Natarajan -- A theorem on summability factors for regular methods in complete ultrametric fields
H. Ochsenius -- Hilbert-like spaces over Krull valued fields
H. Ochsenius and W. H. Schikhof -- Compact operators on non-classical Hilbert spaces
C. Perez-Garcia -- Locally convex spaces over non-archimedean valued fields
C. Perez-Garcia and W. H. Schikhof -- Finite-dimensional orthocomplemented subspaces in p-adic normed spaces
S. Priess-Crampe and P. Ribenboim -- Systems of differential equations over valued fields
J. Rivera-Letelier -- Bi-analytic elements and partial isometries of hyperbolic space
M.-C. Sarmant -- Analytic roots of solutions of p-adic differential equations
K. Shamseddine and M. Berz -- Measure theory and integration on the Levi-Civita field
W. Sliwa -- On block basic sequences in non-archimedean Frechet spaces
P.-A. Svensson -- Dynamical systems in unramified or totally ramified extensions of the p-adic number field
L. van Hamme -- p-adic analysis and the calculus of finite differences

Details:

Series: Contemporary Mathematics, Volume: 319
Publication Year: 2003
ISBN: 0-8218-3320-0
Paging: approximately 432 pp.
Binding: Softcover

Edited by: Anna Kaminska, University of Memphis, TN

Trends in Banach Spaces and Operator Theory

Expected publication date is May 14, 2003

Description

This volume contains proceedings of the conference on Trends in Banach Spaces and Operator Theory, which was devoted to recent advances in theories of Banach spaces and linear operators.

Included in the volume are 25 papers, some of which are expository, while others present new results. The articles address the following topics: history of the famous James' theorem on reflexivity, projective tensor products, construction of noncommutative L_p-spaces via interpolation, Banach spaces with abundance of nontrivial operators, Banach spaces with small spaces of operators, convex geometry of Coxeter-invariant polyhedra, uniqueness of unconditional bases in quasi-Banach spaces, dynamics of cohyponormal operators, and Fourier algebras for locally compact groupoids.

The book is suitable for graduate students and research mathematicians interested in Banach spaces and operator theory and their applications.

Contents

M. D. Acosta, J. B. Guerrero, and M. R. Galan -- Characterizations of the reflexive spaces in the spirit of James' Theorem
F. Albiac, N. J. Kalton, and C. Leranoz -- Uniqueness of unconditional bases in quasi-Banach spaces
G. Androulakis -- A note on the method of minimal vectors
J. Diestel, J. Fourie, and J. Swart -- The projective tensor product I
S. J. Dilworth and V. G. Troitsky -- Spectrum of a weakly hypercyclic operator meets the unit circle
N. S. Feldman -- The dynamics of cohyponormal operators
E. A. Gallardo-Gutierrez and M. J. Gonzalez -- Hilbert-Schmidt composition operators on Dirichlet spaces
N. J. Kalton -- A remark on sectorial operators with an H^{infty}- calculus
J. Kawabe -- Borel injective tensor product and convolution of vector measures and their weak convergence
V. A. Khatskevich and V. S. Shulman -- On linear operator pencils and inclusions of images of balls
D. H. Leung and W.-K. Tang -- Ordinal indices and ell^1-spreading models
J. Lopez-Gomez and C. Mora-Corral -- Characterizing the existence of local Smith forms for mathcal{C}^infty families of matrix operators
N. McCarthy, D. Ogilvie, N. Zobin, and V. Zobin -- Convex geometry of Coxeter-invariant polyhedra
J. Miao -- Commutators on bounded symmetric domains in mathbb{C}^n
T. L. Miller, V. G. Miller, and M. M. Neumann -- Growth conditions and decomposable extensions
J. Moorhouse and C. Toews -- Differences of composition operators
G. A. Munoz -- Complex vs real variables for real 3-homogeneous polynomials on ell_1^2: A counterexample
A. L. T. Paterson -- The Fourier-Stieltjes and Fourier algebras for locally compact groupoids
G. T. Prajitura -- Preserving the commutant under functional calculus
Y. Raynaud -- L_p-spaces associated with a von Neumann algebra without trace: a gentle introduction via complex interpolation
H. P. Rosenthal -- Banach and operator space structure of C^*-algebras
T. Schlumprecht -- How many operators exist on a Banach space?
G. V. Wood -- Maximal algebra norms
A. Zsak -- On Banach spaces with small spaces of operators
A. Zvavitch -- A remark on p-summing norms of operators

Details:

Series: Contemporary Mathematics, Volume: 321
Publication Year: 2003
ISBN: 0-8218-3234-4
Paging: 366 pp.
Binding: Softcover

Robert A. Adams / John J. F. Fournier
University of British Columbia, Vancouver, Canada

Sobolev Spaces, Second Edition

(Pure and Applied Mathematics, Volume 140)

Contents

Includes reviews of real analysis and an extensive treatment of Lebesgue spaces.
Develops at length the intrinsic definition and properties of Sobolev spaces, in particular their imbedding, compact imbedding, interpolation and extension properties.
Provides a thorough treatment of the real interpolation method and its application to Lorentz and Besov spaces.
Includes surveys of other fractional-order spaces (Bessel potentials, Triebel-Lizorkin).
Develops the theory of Orlicz and Orlicz-Sobolev spaces and their imbeddings.

Readership: Graduate students in Mathematics and Applied Mathematics. Researchers in Numerical Analysis and various Physical Sciences.

ISBN: 0-12-044143-8 Book/Hardback

Measurements: 6 X 9 in
Pages: 300

James B. Hartle, University of California, Santa Barbara

Gravity: An Introduction to Einstein's General Relativity

ISBN: 0-8053-8662-9
Copyright: 2003
Format: Cloth; 656 pp

Description
Einstein's theory of general relativity is a cornerstone of modern physics. It also touches upon a wealth of topics that students find fascinating?black holes, warped spacetime, gravitational waves, and cosmology. Until now, it has not been included in the curriculum of many undergraduate physics courses because the required math is too advanced. The aim of this ground-breaking new text is to bring general relativity into the undergraduate curriculum and make this fundamental theory accessible to virtually all physics majors. Using a "physics first" approach to the subject, renowned relativist James Hartle provides a fluent and accessible introduction that uses a minimum of new mathematics and illustrates a wealth of applications.

Recognizing that there is not enough time in a short introductory course to present the traditional, tensor theory approach, James Hartle provides in this book a number of pedagogical innovations.

Buhmann, M.D., Universitat Giessen, Germany,
Mache, D. ,Universitat Dortmund, Germany

Advanced Problems in Constructive Approximation
3rd International Meeting on Approximation Theory (IDoMAT) 2001

International Series of Numerical Mathematics, Vol. 142

2003. 288 pages. Hardcover
ISBN 3-7643-6648-6
English

The current form of modern approximation theory is shaped by many new developments which are the subject of the International Dortmund Meetings on Approximation Theory (IDoMAT). This volume contains refereed articles originating from IDoMAT 2001 that took place in Witten-Bommerholz in August 2001. The contributors are renowned international experts in their individual field of research, including approximation methods, orthogonal polynomials, radial basis functions, multivariate spline approximation and interpolation, Pade approximation, polynomial approximation, and quasi-interpolation. As many applications to areas such as CAD or tomography are discussed, the book should be of interest to both mathematicians and engineers.

Contents

Preface (-) List of Participants (-) Contributions by H. Bavinck, M.G. de Bruin, W. zu Castell, D.H. Mache, F. Fibir, N.L. Fernandez, C. Fredebeul, M. Hollenhorst, V.N. Konovalov, R. Lasser, D. Leviatan, D.S. Lubinsky, H.N. Mhaskar, J. Obermaier, I. Rasa, M. Revers, C.H. Rohwer, P. Sablonniere, R. Schablack, J. Szabados, L. Szili, R. Szwarc, V. Totic, P. Vertesi, H. Wendland

Hernandez-Lerma, O., Departamento de Matematicas, CINVESTAV-IPN, Mexico
Lasserre, J.B., LAAS-CNRS, Toulouse, France (Eds.)

Markov Chains and Invariant Probabilities

Progress in Mathematics, Vol. 211
2003. 224 pages. Hardcover
ISBN 3-7643-7000-9
English

This book concerns discrete-time homogeneous Markov chains that admit an invariant probability measure.

The main objective is to give a systematic, self-contained presentation on some key issues about the ergodic behavior of that class of Markov chains. These issues include, in particular, the various types of convergence of expected and pathwise occupation measures, and ergodic decompositions of the state space. Some of the results presented appear for the first time in book form. A distinguishing feature of the book is the emphasis on the role of expected occupation measures to study the long-run behavior of Markov chains on uncountable spaces. The intended audience are graduate students and researchers in theoretical and applied probability, operations research, engineering and economics.