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Functional Analysis papers — page 6

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Fourier Duality as a Quantization Principle
The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac…
R. Aldrovandi, L. A. SaegerAug 27, 1996
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Projective Fourier Duality and Weyl Quantization
The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for noncommutative Fourier…
R. Aldrovandi, L. A. SaegerAug 27, 1996
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Operator of fractional derivative in the complex plane
The paper deals with a fractional derivative introduced by means of the Fourier transform. The explicit form of the kernel of general derivative operator acting on the functions analytic on a curve…
P. ZavadaAug 12, 1996
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Quantized Kronecker flows and almost periodic quantum field theory
We define and study the properties of the infinite dimensional quantized Kronecker flow. This *-dynamical system arises as a quantization of the corresponding flow on an infinite dimensional…
Slawomir Klimek, Andrzej LesniewskiAug 12, 1996
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The stable rank of some free product C*-algebras
It is proved that the reduced group C*-algebra C*red(G) has stable rank one (i.e. its group of invertible elements is a dense subset) if G is a discrete group arising as a free product G1*G2…
Ken Dykema, Uffe Haagerup, Mikael RordamAug 9, 1996
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Abundance of invariant and almost invariant pure states of C*-dynamical systems
We show that invariant states of C*-dynamical systems can be approximated in the weak*-topology by invariant pure states, or almost invariant pure states, under various circumstances.
Ola Bratteli, Akitaka Kishimoto, Derek W. RobinsonJul 29, 1996
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On self-adjointness of a Schroedinger operator
Let M be a complete Riemannian manifold and let Ω*(M) denote the space of differential forms on M. Let d:Ω*(M) Ω*+1(M) be the exterior differential operator and let =dd*+d*d…
Maxim BravermanJul 28, 1996
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Covariant SPDEs and Quantum Field Structures
Covariant stochastic partial differential equations are studied in any dimension. A special class of such equations is selected and it is proven that the solutions can be analytically continued to…
C. Becker, R. Gielerak, P. ŁugiewiczJul 4, 1996
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Homology of pseudodifferential operators I. Manifolds with boundary
The Hochschild and cyclic homology groups are computed for the algebra of `cusp' pseudodifferential operators on any compact manifold with boundary. The index functional for this algebra is…
Richard B. Melrose, Victor NistorJun 21, 1996
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Super-connections and non-commutative geometry
We show that Quillen's formalism for computing the Chern character of the index using superconnections extends to arbitrary operators with functional calculus. We thus remove the condition that…
Victor NistorJun 14, 1996
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Node Theorem for Matrix Schroedinger Operators
In this paper we study the ground states of a matrix Schroedinger operator, that is an operator of the type (-Laplace) + V acting on m-component wave functions in Rn. We prove in generalization of…
Felix FinsterJun 14, 1996
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Removal of the resolvent-like energy dependence from interactions and invariant subspaces of a total Hamiltonian
The spectral problem (A + V(z))ψ=zψ is considered where the main Hamiltonian A is a self-adjoint operator of sufficiently arbitrary nature. The perturbation V(z)=-B(A'-z)-1B* depends…
A. K. MotovilovJun 12, 1996
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An Introduction to K-theory and Cyclic Cohomology
These lecture notes contain an exposition of basic ideas of K-theory and cyclic cohomology. I begin with a list of examples of various situations in which the K-functor of Grothendieck appears…
Jacek BrodzkiJun 3, 1996
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Topological Hilbert Nullstellensatz for Bergman Spaces
The results in the paper are related to the classification problem for invariant subspaces of multiplication operators in several variables. The main results consist of characterizations, in the two…
Razvan GelcaMay 10, 1996
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Two applications of free entropy
Using Voiculsecu's free entropy, it is shown that the free group factors L(Fn) lack property C of Popa and that they lack finite multiplicity abelian subalgebras. Property C is an assymptotic…
Ken DykemaMay 8, 1996
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Hilbert H*-modules and Hilbert modules over (non-self-adjoint) operator algebras -- a reference overview II
The two reference lists contain 54/22 references of papers and preprints concerned with the theory and/or various applications of Hilbert modules over Hilbert *-algebras and over (non-self-adjoint)…
Michael FrankMay 7, 1996
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Hilbert C*-modules and related subjects - a guided reference overview I
The overview contains 450 references of books, chapters of monographs, papers, preprints and Ph.~D.~thesises which are concerned with the theory and/or various applications of Hilbert C*-modules. To…
Michael FrankMay 7, 1996
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The :ϕ44: quantum field theory, I. Wave operator, holomorphity and Wick kernel
With the help of the complex structure and the wave operator of the nonlinear classical Klein-Gordon equation with the interaction u44 we define the Wick kernel of the interacting quantum field…
Edward P. OsipovMay 7, 1996
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Diagonalizing operators over continuous fields of C*-algebras
It is well known that in the commutative case, i.e. for A=C(X) being a commutative C*-algebra, compact selfadjoint operators acting on the Hilbert C*-module HA (= continuous families of such…
V. M. ManuilovMay 4, 1996
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R-diagonal pairs - a common approach to Haar unitaries and circular elements
In the free probability theory of Voiculescu two of the most frequently used *-distributions are those of a Haar unitary and of a circular element. We define an R-diagonal pair as a generalization…
Alexandru Nica, Roland SpeicherApr 30, 1996
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On the multiplication of free n-tuples of non-commutative random variables
Let a1,...,an, b1,...,bn be random variables in some (non-commutative) probability space, such that \a1, ..., an \ is free from \b1, ..., bn \. We show how the joint…
Alexandru Nica, Roland SpeicherApr 30, 1996
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q-Gaussian processes: non-commutative and classical aspects
We examine, for -1<q<1, q-Gaussian processes, i.e. families of operators (non-commutative random variables) Xt=at+at* -- where the at fulfill the q-commutation relations…
Marek Bozejko, Burkhard Kummerer, Roland SpeicherApr 30, 1996
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Amenability for Fell Bundles
Given a Fell bundle , over a discrete group Γ, we construct its reduced cross sectional algebra C*r(), in analogy with the reduced crossed products defined for C*-dynamical systems. When…
Ruy ExelApr 23, 1996
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A Theory of Dimension
In which a theory of dimension related to the Jones index and based on the notion of conjugation is developed. An elementary proof of the additivity and multiplicativity of the dimension is given and…
Roberto Longo, John E. RobertsApr 17, 1996
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Compact Perturbations of Fredholm n-tuples II
The paper contains examples of Fredholm n-tuples of operators that are of index 0 but cannot be perturbed by compact operators to n-tuples with exact Koszul complex.
Razvan GelcaApr 10, 1996
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