Extension Of Positive Definite Distributions And Maximum Entropy

Author : Jean-Pierre Gabardo
Publisher : American Mathematical Soc.
Page : 94 pages
File Size : 40,6 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825518

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Extension of Positive-Definite Distributions and Maximum Entropy by Jean-Pierre Gabardo Pdf

In this work, the maximum entropy method is used to solve the extension problem associated with a positive-definite function, or distribution, defined on an interval of the real line. Garbardo computes explicitly the entropy maximizers corresponding to various logarithmic integrals depending on a complex parameter and investigates the relation to the problem of uniqueness of the extension. These results are based on a generalization, in both the discrete and continuous cases, of Burg's maximum entropy theorem.

Author : Jean-Pierre Gabardo
Publisher : American Mathematical Society(RI)
Page : 111 pages
File Size : 52,9 Mb
Release : 2014-08-31
Category : Fourier analysis
ISBN : 1470400669

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Extension of Positive-Definite Distributions and Maximum Entropy. by Jean-Pierre Gabardo Pdf

In this work, the maximum entropy method is used to solve the extension problem associated with a positive-definite function, or distribution, defined on an interval of the real line. Garbardo computes explicitly the entropy maximizers corresponding to various logarithmic integrals depending on a complex parameter and investigates the relation to the problem of uniqueness of the extension. These results are based on a generalization, in both the discrete and continuous cases, of Burg's maximum entropy theorem.

Author : J.S. Byrnes,Kathryn A. Hargreaves,Karl Berry
Publisher : Springer Science & Business Media
Page : 688 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401127912

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Probabilistic and Stochastic Methods in Analysis, with Applications by J.S. Byrnes,Kathryn A. Hargreaves,Karl Berry Pdf

Probability has been an important part of mathematics for more than three centuries. Moreover, its importance has grown in recent decades, since the computing power now widely available has allowed probabilistic and stochastic techniques to attack problems such as speech and image processing, geophysical exploration, radar, sonar, etc. -- all of which are covered here. The book contains three exceptionally clear expositions on wavelets, frames and their applications. A further extremely active current research area, well covered here, is the relation between probability and partial differential equations, including probabilistic representations of solutions to elliptic and parabolic PDEs. New approaches, such as the PDE method for large deviation problems, and stochastic optimal control and filtering theory, are beginning to yield their secrets. Another topic dealt with is the application of probabilistic techniques to mathematical analysis. Finally, there are clear explanations of normal numbers and dynamic systems, and the influence of probability on our daily lives.

Author : Cristiano Husu
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 41,6 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825716

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Extensions of the Jacobi Identity for Vertex Operators, and Standard $A^{(1)}_1$-Modules by Cristiano Husu Pdf

This book extends the Jacobi identity, the main axiom for a vertex operator algebra, to multi-operator identities. Based on constructions of Dong and Lepowsky, relative ${\mathbf Z}_2$-twisted vertex operators are then introduced, and a Jacobi identity for these operators is established. Husu uses these ideas to interpret and recover the twisted Z -operators and corresponding generating function identities developed by Lepowsky and Wilson for the construction of the standard $A^{(1)}_1$-modules. The point of view of the Jacobi identity also shows the equivalence between these twisted Z-operator algebras and the (twisted) parafermion algebras constructed by Zamolodchikov and Fadeev. The Lepowsky-Wilson generating function identities correspond to the identities involved in the construction of a basis for the space of C-disorder fields of such parafermion algebras.

Author : André Joyal,Myles Tierney
Publisher : American Mathematical Soc.
Page : 71 pages
File Size : 52,6 Mb
Release : 1984
Category : Mathematics
ISBN : 9780821823125

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An Extension of the Galois Theory of Grothendieck by André Joyal,Myles Tierney Pdf

Author : William M. McGovern
Publisher : American Mathematical Soc.
Page : 67 pages
File Size : 49,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825808

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Completely Prime Maximal Ideals and Quantization by William M. McGovern Pdf

This monograph will appeal to graduate students and researchers interested in Lie algebras. McGovern classifies the completely prime maximal spectrum of the enveloping algebra of any classical semisimple Lie algebra. He also studies finite algebra extensions of completely prime primitive quotients of such enveloping algebras and computes their lengths as bimodules, characteristic cycles, and Goldie ranks in many cases. This work marks a major advance in the quantization program, which seeks to extend the methods of (commutative) algebraic geometry to the setting of enveloping algebras. While such an extension cannot be completely carried out, this work shows that many partial results are available.

Author : Takashi Shioya
Publisher : American Mathematical Soc.
Page : 73 pages
File Size : 49,6 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825785

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Behavior of Distant Maximal Geodesics in Finitely Connected Complete 2-dimensional Riemannian Manifolds by Takashi Shioya Pdf

This monograph studies the topological shapes of geodesics outside a large compact set in a finitely connected, complete, and noncompact surface admitting total curvature. When the surface is homeomorphic to a plane, all such geodesics behave like those of a flat cone. In particular, the rotation numbers of the geodesics are controlled by the total curvature. Accessible to beginners in differential geometry, but also of interest to specialists, this monograph features many illustrations that enhance understanding of the main ideas.

Author : Jacek Nikiel,H. M. Tuncali,E. D. Tymchatyn
Publisher : American Mathematical Soc.
Page : 80 pages
File Size : 51,9 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825617

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Continuous Images of Arcs and Inverse Limit Methods by Jacek Nikiel,H. M. Tuncali,E. D. Tymchatyn Pdf

Continuous images of ordered continua have been studied intensively since 1960, when S. Mardsic showed that the classical Hahn-Mazurkiewicz theorem does not generalize in the ``natural'' way to the nonmetric case. In 1986, Nikiel characterized acyclic images of arcs as continua which can be approximated from within by a sequence of well-placed subsets which he called T-sets. That characterization has been used to answer a host of outstanding questions in the area. In this book, Nikiel, Tymchatyn, and Tuncali study images of arcs using T-set approximations and inverse limits with monotone bonding maps. A number of important theorems on Peano continua are extended to images of arcs. Some of the results presented here are new even in the metric case.

Author : Svante Janson
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 43,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825952

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Orthogonal Decompositions and Functional Limit Theorems for Random Graph Statistics by Svante Janson Pdf

This book develops a method to obtain limit theorems for various functionals of random graphs. The method is based on a certain orthogonal decomposition. Janson's results include limit theorems for the two standard random graph models, $G_{n,p}$ and $G_{n,m}$, as well as functional limit theorems for the evolution of a random graph and results on the maximum of a function during the evolution. Janson obtains both normal and nonnormal limits, and the method provides an explanation for the appearance of nonnormal limits. Applications to subgraph counts and to vertex degrees are presented as examples.

Author : Hans Plesner Jakobsen
Publisher : American Mathematical Soc.
Page : 129 pages
File Size : 52,7 Mb
Release : 1994
Category : Hilbert space
ISBN : 9780821825938

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The Full Set of Unitarizable Highest Weight Modules of Basic Classical Lie Superalgebras by Hans Plesner Jakobsen Pdf

This work contains a complete description of the set of all unitarizable highest weight modules of classical Lie superalgebras. Unitarity is defined in the superalgebraic sense, and all the algebras are over the complex numbers. Part of the classification determines which real forms, defined by anti-linear anti-involutions, may occur. Although there have been many investigations for some special superalgebras, this appears to be the first systematic study of the problem.

Author : Yongsheng Han,Eric T. Sawyer
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 44,9 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825921

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Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces by Yongsheng Han,Eric T. Sawyer Pdf

In this work, Han and Sawyer extend Littlewood-Paley theory, Besov spaces, and Triebel-Lizorkin spaces to the general setting of a space of homogeneous type. For this purpose, they establish a suitable analogue of the Calder 'on reproducing formula and use it to extend classical results on atomic decomposition, interpolation, and T1 and Tb theorems. Some new results in the classical setting are also obtained: atomic decompositions with vanishing b-moment, and Littlewood-Paley characterizations of Besov and Triebel-Lizorkin spaces with only half the usual smoothness and cancellation conditions on the approximate identity.

Author : Neal W. Stoltzfus
Publisher : American Mathematical Soc.
Page : 91 pages
File Size : 45,9 Mb
Release : 1977
Category : Mathematics
ISBN : 9780821821923

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Unraveling the Integral Knot Concordance Group by Neal W. Stoltzfus Pdf

The group of concordance classes of high dimensional homotopy spheres knotted in codimension two in the standard sphere has an intricate algebraic structure which this paper unravels. The first level of invariants is given by the classical Alexander polynomial. By means of a transfer construction, the integral Seifert matrices of knots whose Alexander polynomial is a power of a fixed irreducible polynomial are related to forms with the appropriate Hermitian symmetry on torsion free modules over an order in the algebraic number field determined by the Alexander polynomial. This group is then explicitly computed in terms of standard arithmetic invariants. In the symmetric case, this computation shows there are no elements of order four with an irreducible Alexander polynomial. Furthermore, the order is not necessarily Dedekind and non-projective modules can occur. The second level of invariants is given by constructing an exact sequence relating the global concordance group to the individual pieces described above. The integral concordance group is then computed by a localization exact sequence relating it to the rational group computed by J. Levine and a group of torsion linking forms.

Author : Hongbing Su
Publisher : American Mathematical Soc.
Page : 83 pages
File Size : 51,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821826072

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On the Classification of $C^*$-algebras of Real Rank Zero: Inductive Limits of Matrix Algebras over Non-Hausdorff Graphs by Hongbing Su Pdf

This work shows that $K$-theoretic data is a complete invariant for certain inductive limit $C^*$-algebras. $C^*$-algebras of this kind are useful in studying group actions. Su gives a $K$-theoretic classification of the real rank zero $C^*$-algebras that can be expressed as inductive limits of finite direct sums of matrix algebras over finite (possibly non-Hausdorff) graphs or Hausdorff one-dimensional spaces defined as inverse limits of finite graphs. In addition, Su establishes a characterization for an inductive limit of finite direct sums of matrix algebras over finite (possibly non-Hausdorff) graphs to be real rank zero.

Author : Tom Ilmanen
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 50,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825822

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Elliptic Regularization and Partial Regularity for Motion by Mean Curvature by Tom Ilmanen Pdf

This monograph considers (singular) surfaces moving by mean curvature, combining tools of geometric measure theory with ``viscosity solution'' techniques. Employing the geometrically natural concept of ``elliptic regularization'', Ilmanen establishes the existence of these surfaces. The ground-breaking work of Brakke, combined with the recently developed ``level-set'' approach, yields surfaces moving by mean curvature that are smooth almost everywhere. The methods developed here should form a foundation for further work in the field. This book is also noteworthy for its especially clear exposition and for an introductory chapter summarizing the key compactness theorems of geometric measure theory.

Author : Arthur Erdélyi,Charles Andrew Swanson
Publisher : American Mathematical Soc.
Page : 50 pages
File Size : 43,8 Mb
Release : 1957
Category : Mathematics
ISBN : 9780821812259

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Asymptotic Forms of Whittaker's Confluent Hypergeometric Functions by Arthur Erdélyi,Charles Andrew Swanson Pdf