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The Finite Calculus Associated with Bessel Functions
Although Bessel functions are among the most widely used functions in applied mathematics, this book is essentially the first to present a calculus associated with this class of functions. The author obtains a generalized umbral calculus associated with the Euler operator and its associated Bessel eigenfunctions for each positive value of an index parameter. For one particular value of this parameter, the functions and operators can be associated with the radial parts of $n$-dimensional Euclidean space objects. Some of the results of this book are in part extensions of the work of Rota and his co-workers on the ordinary umbral calculus and binomial enumeration. The author also introduces a wide variety of new polynomial sequences together with their groups and semigroup compositional properties. Generalized Bernoulli, Euler, and Stirling numbers associated with Bessel functions and the corresponding classes of polynomials are also studied. The book is intended for mathematicians and physicists at the research level in special function theory.
Primes Associated to an Ideal
Discusses five closely related sets of prime ideals associated to an ideal I in a Noetherian ring, the persistent, asymptotic, quintasymptotic, essential, and quintessential primes of I. Requires a standard year course in commutative ring theory. Annotation copyright Book News, Inc. Portland, Or.
Spinor Construction of Vertex Operator Algebras, Triality, and $E^{(1)}_8$
The theory of vertex operator algebras is a remarkably rich new mathematical field which captures the algebraic content of conformal field theory in physics. Ideas leading up to this theory appeared in physics as part of statistical mechanics and string theory. In mathematics, the axiomatic definitions crystallized in the work of Borcherds and in Vertex Operator Algebras and the Monster, by Frenkel, Lepowsky, and Meurman. The structure of monodromies of intertwining operators for modules of vertex operator algebras yield braid group representations and leads to natural generalizations of vertex operator algebras, such as superalgebras and para-algebras. Many examples of vertex operator algeb...
The Lefschetz Centennial Conference
This volume contains many of the papers in the area of differential equations presented at the 1984 Solomon Lefschetz Centennial Conference held in Mexico City.
Index Theory of Elliptic Operators, Foliations, and Operator Algebras
Combining analysis, geometry, and topology, this volume provides an introduction to current ideas involving the application of $K$-theory of operator algebras to index theory and geometry. In particular, the articles follow two main themes: the use of operator algebras to reflect properties of geometric objects and the application of index theory in settings where the relevant elliptic operators are invertible modulo a $C^*$-algebra other than that of the compact operators. The papers in this collection are the proceedings of the special sessions held at two AMS meetings: the Annual meeting in New Orleans in January 1986, and the Central Section meeting in April 1986. Jonathan Rosenberg's exposition supplies the best available introduction to Kasparov's $KK$-theory and its applications to representation theory and geometry. A striking application of these ideas is found in Thierry Fack's paper, which provides a complete and detailed proof of the Novikov Conjecture for fundamental groups of manifolds of non-positive curvature. Some of the papers involve Connes' foliation algebra and its $K$-theory, while others examine $C^*$-algebras associated to groups and group actions on spaces.
Algebraic K-theory and Algebraic Number Theory
This volume contains the proceedings of a seminar on Algebraic $K$-theory and Algebraic Number Theory, held at the East-West Center in Honolulu in January 1987. The seminar, which hosted nearly 40 experts from the U.S. and Japan, was motivated by the wide range of connections between the two topics, as exemplified in the work of Merkurjev, Suslin, Beilinson, Bloch, Ramakrishnan, Kato, Saito, Lichtenbaum, Thomason, and Ihara. As is evident from the diversity of topics represented in these proceedings, the seminar provided an opportunity for mathematicians from both areas to initiate further interactions between these two areas.
Methods and Applications of Mathematical Logic
Constitutes the proceedings of the Seventh Latin American Symposium on Mathematical Logic, held July 29-August 2, 1985, at the University of Campinas in Brazil. This book offers an introduction to the active lines of research in mathematical logic and emphasizes the connections to other fields - philosophy, computer science and probability theory.
Geometry of Group Representations
Contains papers based on talks delivered at the AMS-IMS-SIAM Summer Research Conference on the Geometry of Group Representations, held at the University of Colorado in Boulder in July 1987. This work offers an understanding of the state of research in the geometry of group representations and their applications.
Differential Geometry: The Interface between Pure and Applied Mathematics
Contains papers that represent the proceedings of a conference entitled 'Differential Geometry: The Interface Between Pure and Applied Mathematics', which was held in San Antonio, Texas, in April 1986. This work covers a range of applications and techniques in such areas as ordinary differential equations, Lie groups, algebra and control theory.
