7,599 research outputs found
Functional models for Nevanlinna families
The class of Nevanlinna families consists of -symmetric holomorphic multivalued functions on with maximal dissipative (maximal accumulative) values on (, respectively) and is a generalization of the class of operator-valued Nevanlinna functions. In this note Nevanlinna families are realized as Weyl families of boundary relations induced by multiplication operators with the independent variable in reproducing kernel Hilbert spaces
A distributional approach to the geometry of dislocations at the mesoscale
We develop a theory to represent dislocated single crystals at the mesoscopic
scale by considering concentrated effects, governed by the distribution theory
combined with multiple-valued kinematic fields. Our approach gives a new
understanding of the continuum theory of defects as developed by Kroener (1980)
and other authors. Fundamental 2D identities relating the incompatibility
tensor to the Frank and Burgers vectors are proved under global strain
assumptions relying on the geometric measure theory, thereby giving rise to
rigorous homogenisation from mesoscopic to macroscopic scale.Comment: article soumi
Operator Formalism on General Algebraic Curves
The usual Laurent expansion of the analytic tensors on the complex plane is
generalized to any closed and orientable Riemann surface represented as an
affine algebraic curve. As an application, the operator formalism for the
systems is developed. The physical states are expressed by means of creation
and annihilation operators as in the complex plane and the correlation
functions are evaluated starting from simple normal ordering rules. The Hilbert
space of the theory exhibits an interesting internal structure, being splitted
into ( is the number of branches of the curve) independent Hilbert
spaces. Exploiting the operator formalism a large collection of explicit
formulas of string theory is derived.Comment: 34 pages of plain TeX + harvmac, With respect to the first version
some new references have been added and a statement in the Introduction has
been change
Multivalued Fields on the Complex Plane and Conformal Field Theories
In this paper a class of conformal field theories with nonabelian and
discrete group of symmetry is investigated. These theories are realized in
terms of free scalar fields starting from the simple systems and scalar
fields on algebraic curves. The Knizhnik-Zamolodchikov equations for the
conformal blocks can be explicitly solved. Besides of the fact that one obtains
in this way an entire class of theories in which the operators obey a
nonstandard statistics, these systems are interesting in exploring the
connection between statistics and curved space-times, at least in the two
dimensional case.Comment: (revised version), 30 pages + one figure (not included), (requires
harvmac.tex), LMU-TPW 92-1
Dirichlet-to-Neumann maps on bounded Lipschitz domains
The Dirichlet-to-Neumann map associated to an elliptic partial differential
equation becomes multivalued when the underlying Dirichlet problem is not
uniquely solvable. The main objective of this paper is to present a systematic
study of the Dirichlet-to-Neumann map and its inverse, the Neumann-to-Dirichlet
map, in the framework of linear relations in Hilbert spaces. Our treatment is
inspired by abstract methods from extension theory of symmetric operators,
utilizes the general theory of linear relations and makes use of some deep
results on the regularity of the solutions of boundary value problems on
bounded Lipschitz domains
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