Quantum Integrable Systems
Analytic Hilbert Modules
Recent developments in the Navier-Stokes problem
The Structure of Complex Lie Groups
Morse Theory for Hamiltonian Systems
By Dorothee D. Haroske
October 18, 2019
Until now, no book has systematically presented the recently developed concept of envelopes in function spaces. Envelopes are relatively simple tools for the study of classical and more complicated spaces, such as Besov and Triebel-Lizorkin types, in limiting situations. This theory originates from...
By Detlef Lehmann
September 05, 2019
Mathematical Methods of Many-Body Quantum Field Theory offers a comprehensive, mathematically rigorous treatment of many-body physics. It develops the mathematical tools for describing quantum many-body systems and applies them to the many-electron system. These tools include the formalism of ...
By Asesh Roy Chowdhury, Aninlya Ghose Choudhury
January 28, 2004
The study of integrable systems has opened new horizons in classical physics over the past few decades, particularly in the subatomic world. Yet despite the field now having reached a level of maturity, very few books provide an introduction to the field accessible to specialists and nonspecialists...
By Xiaoman Chen, Kunyu Guo
March 26, 2003
The seminal 1989 work of Douglas and Paulsen on the theory of analytic Hilbert modules precipitated a number of major research efforts. This in turn led to some intriguing and valuable results, particularly in the areas of operator theory and functional analysis. With the field now beginning to ...
By Pierre Gilles Lemarie-Rieusset
April 26, 2002
The Navier-Stokes equations: fascinating, fundamentally important, and challenging,. Although many questions remain open, progress has been made in recent years. The regularity criterion of Caffarelli, Kohn, and Nirenberg led to many new results on existence and non-existence of solutions, and the ...
By Dong Hoon Lee
August 31, 2001
Complex Lie groups have often been used as auxiliaries in the study of real Lie groups in areas such as differential geometry and representation theory. To date, however, no book has fully explored and developed their structural aspects.The Structure of Complex Lie Groups addresses this need. ...
By Reynaldo Rocha-Chavez, Michael Shapiro, Frank Sommen
August 03, 2001
The theory of holomorphic functions of several complex variables emerged from the attempt to generalize the theory in one variable to the multidimensional situation. Research in this area has led to the discovery of many sophisticated facts, structures, ideas, relations, and applications. This ...
By Roland Potthast
May 30, 2001
Over the last twenty years, the growing availability of computing power has had an enormous impact on the classical fields of direct and inverse scattering. The study of inverse scattering, in particular, has developed rapidly with the ability to perform computational simulations of scattering ...
By Julian Lopez-Gomez
March 28, 2001
This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. It features the construction of an optimal algebraic/analytic invariant for ...
By L.J. Mason, P.Z. Kobak, L. Hughston, K. Pulverer
March 15, 2001
Although twistor theory originated as an approach to the unification of quantum theory and general relativity, twistor correspondences and their generalizations have provided powerful mathematical tools for studying problems in differential geometry, nonlinear equations, and representation theory. ...
By Alberto Abbondandolo
March 15, 2001
This Research Note explores existence and multiplicity questions for periodic solutions of first order, non-convex Hamiltonian systems. It introduces a new Morse (index) theory that is easier to use, less technical, and more flexible than existing theories and features techniques and results that, ...
By Vijay Kodiyalam, V.S. Sunder
December 07, 2000
Pure mathematicians have only recently begun a rigorous study of topological quantum field theories (TQFTs). Ocneanu, in particular, showed that subfactors yield TQFTs that complement the Turaev-Viro construction. Until now, however, it has been difficult to find an account of this work that is ...