Author: Ola BratteliPublisher: American Mathematical Soc.
ISBN: 0821809628
Category : C*-algebras
Languages : en
Pages : 106
Book Description
This book is intended for graduate students and research mathematicians working in functional analysis.
Iterated Function Systems and Permutation Representations of the Cuntz Algebra
Author: Ola BratteliPublisher: American Mathematical Soc.
ISBN: 0821809628
Category : C*-algebras
Languages : en
Pages : 106
Book Description
This book is intended for graduate students and research mathematicians working in functional analysis.
Operator Algebras, Operator Theory and Applications
Author: Maria Amélia BastosPublisher: Springer Science & Business Media
ISBN: 3764386843
Category : Mathematics
Languages : en
Pages : 437
Book Description
This book is composed of three survey lecture courses and some twenty invited research papers presented to WOAT 2006 - the International Summer School and Workshop on Operator Algebras, Operator Theory and Applications, held at Lisbon in September 2006. The volume reflects recent developments in the area of operator algebras and their interaction with research fields in complex analysis and operator theory. The book is aimed at postgraduates and researchers in these fields.
Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes
Author: Daniel AlpayPublisher: Birkhäuser
ISBN: 3319103350
Category : Mathematics
Languages : en
Pages : 394
Book Description
The volume is dedicated to Lev Sakhnovich, who made fundamental contributions in operator theory and related topics. Besides bibliographic material, it includes a number of selected papers related to Lev Sakhnovich's research interests. The papers are related to operator identities, moment problems, random matrices and linear stochastic systems.
Ruelle Operators: Functions which Are Harmonic with Respect to a Transfer Operator
Author: Palle E. T. JørgensenPublisher: American Mathematical Soc.
ISBN: 0821826883
Category : Memoirs of the American Mathematical Society
Languages : en
Pages : 74
Book Description
Let $N\in\mathbb{N}$, $N\geq2$, be given. Motivated by wavelet analysis, this title considers a class of normal representations of the $C DEGREES{\ast}$-algebra $\mathfrak{A}_{N}$ on two unitary generators $U$, $V$ subject to the relation $UVU DEGREES{-1}=V DEGREES{N}$. The representations are in one-to-one correspondence with solutions $h\in L DEGREES{1}\left(\mathbb{T}\right)$, $h\geq0$, to $R\left(h\right)=h$ where $R$ is a certain transfer operator (positivity-preserving) which was studied previously by D. Ruelle. The representations of $\mathfrak{A}_{N}$ may also be viewed as representations of a certain (discrete) $N$-adic $ax+b$ group which was considered recently
Representation Theory and Numerical AF-invariants
Author: Ola BratteliPublisher: American Mathematical Soc.
ISBN: 0821834916
Category : Mathematics
Languages : en
Pages : 178
Book Description
Let $\mathcal{O}_{d}$ be the Cuntz algebra on generators $S_{1},\dots,S_{d}$, $2\leq d
Operator Theory, Systems Theory and Scattering Theory: Multidimensional Generalizations
Author: Daniel AlpayPublisher: Springer Science & Business Media
ISBN: 3764373032
Category : Mathematics
Languages : en
Pages : 312
Book Description
This volume contains a selection of papers, from experts in the area, on multidimensional operator theory. Topics considered include the non-commutative case, function theory in the polydisk, hyponormal operators, hyperanalytic functions, and holomorphic deformations of linear differential equations. Operator Theory, Systems Theory and Scattering Theory will be of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.
Frames, Bases and Group Representations
Author: Deguang HanPublisher: American Mathematical Soc.
ISBN: 0821820672
Category : Frames
Languages : en
Pages : 111
Book Description
This work develops an operator-theoretic approach to discrete frame theory on a separable Hilbert space. It is then applied to an investigation of the structural properties of systems of unitary operators on Hilbert space which are related to orthonormal wavelet theory. Also obtained are applications of frame theory to group representations, and of the theory of abstract unitary systems to frames generated by Gabor type systems.
Featured Reviews in Mathematical Reviews 1997-1999
Author: Donald G. BabbittPublisher: American Mathematical Soc.
ISBN: 9780821896709
Category : Mathematics
Languages : en
Pages : 762
Book Description
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.
Quantum Linear Groups and Representations of $GL_n({\mathbb F}_q)$
Author: Jonathan BrundanPublisher: American Mathematical Soc.
ISBN: 0821826166
Category : Group schemes
Languages : en
Pages : 127
Book Description
We give a self-contained account of the results originating in the work of James and the second author in the 1980s relating the representation theory of GL[n(F[q) over fields of characteristic coprime to q to the representation theory of "quantum GL[n" at roots of unity. The new treatment allows us to extend the theory in several directions. First, we prove a precise functorial connection between the operations of tensor product in quantum GL[n and Harish-Chandra induction in finite GL[n. This allows us to obtain a version of the recent Morita theorem of Cline, Parshall and Scott valid in addition for p-singular classes. From that we obtain simplified treatments of various basic known facts, such as the computation of decomposition numbers and blocks of GL[n(F[q) from knowledge of the same for the quantum group, and the non-defining analogue of Steinberg's tensor product theorem. We also easily obtain a new double centralizer property between GL[n(F[[q) and quantum GL[n, generalizing a result of Takeuchi. Finally, we apply the theory to study the affine general linear group, following ideas of Zelevinsky in characteristic zero. We prove results that can be regarded as the modular analogues of Zelevinsky's and Thoma's branching rules. Using these, we obtain a new dimension formula for the irreducible cross-characteristic representations of GL[n(F[q), expressing their dimensions in terms of the characters of irreducible modules over the quantum group.
Introduction To The Theory Of
Author: Vasyl OstrovskyiPublisher: CRC Press
ISBN: 9789058230423
Category : Mathematics
Languages : en
Pages : 272
Book Description
Provides the fundamentals of representations of finitely presented *-algebras by bounded operators. The theory is illustrated with numerous examples of *-algebra. The examples, in particular, include *-algebra with two self-adjoint generators that satisfy a quadratic or a more general relation, *-algebra with three or four generators, *-algebra that arise from one- and many-dimensional discrete dynamical systems. Wick *-algebra various; *-wild algebras. This book is intended for graduate students as well as researchers.