420 research outputs found
Canonical, squeezed and fermionic coherent states in a right quaternionic Hilbert space with a left multiplication on it
Using a left multiplication defined on a right quaternionic Hilbert space, we
shall demonstrate that various classes of coherent states such as the canonical
coherent states, pure squeezed states, fermionic coherent states can be defined
with all the desired properties on a right quaternionic Hilbert space. Further,
we shall also demonstrate squeezed states can be defined on the same Hilbert
space, but the noncommutativity of quaternions prevents us in getting the
desired results.Comment: Conference paper. arXiv admin note: text overlap with
arXiv:1704.02946; substantial text overlap with arXiv:1706.0068
Boundary interpolation for slice hyperholomorphic Schur functions
A boundary Nevanlinna-Pick interpolation problem is posed and solved in the
quaternionic setting. Given nonnegative real numbers , quaternions all of modulus , so that the
-spheres determined by each point do not intersect and for , and quaternions , we wish to find a slice
hyperholomorphic Schur function so that and
Our arguments relies on the theory of slice hyperholomorphic
functions and reproducing kernel Hilbert spaces
The importance of protein expression sod2 in response to oxidative stress for different cancer cells
de Branges-Rovnyak spaces: basics and theory
For a contractive analytic operator-valued function on the unit disk
, de Branges and Rovnyak associate a Hilbert space of analytic
functions and related extension space
consisting of pairs of analytic functions on the unit disk . This
survey describes three equivalent formulations (the original geometric de
Branges-Rovnyak definition, the Toeplitz operator characterization, and the
characterization as a reproducing kernel Hilbert space) of the de
Branges-Rovnyak space , as well as its role as the underlying
Hilbert space for the modeling of completely non-isometric Hilbert-space
contraction operators. Also examined is the extension of these ideas to handle
the modeling of the more general class of completely nonunitary contraction
operators, where the more general two-component de Branges-Rovnyak model space
and associated overlapping spaces play key roles. Connections
with other function theory problems and applications are also discussed. More
recent applications to a variety of subsequent applications are given in a
companion survey article
Applications of Hilbert Module Approach to Multivariable Operator Theory
A commuting -tuple of bounded linear operators on a
Hilbert space \clh associate a Hilbert module over
in the following sense: where and
. A companion survey provides an introduction to the theory
of Hilbert modules and some (Hilbert) module point of view to multivariable
operator theory. The purpose of this survey is to emphasize algebraic and
geometric aspects of Hilbert module approach to operator theory and to survey
several applications of the theory of Hilbert modules in multivariable operator
theory. The topics which are studied include: generalized canonical models and
Cowen-Douglas class, dilations and factorization of reproducing kernel Hilbert
spaces, a class of simple submodules and quotient modules of the Hardy modules
over polydisc, commutant lifting theorem, similarity and free Hilbert modules,
left invertible multipliers, inner resolutions, essentially normal Hilbert
modules, localizations of free resolutions and rigidity phenomenon.
This article is a companion paper to "An Introduction to Hilbert Module
Approach to Multivariable Operator Theory".Comment: 46 pages. This is a companion paper to arXiv:1308.6103. To appear in
Handbook of Operator Theory, Springe
Translation Representations and Scattering By Two Intervals
Studying unitary one-parameter groups in Hilbert space (U(t),H), we show that
a model for obstacle scattering can be built, up to unitary equivalence, with
the use of translation representations for L2-functions in the complement of
two finite and disjoint intervals.
The model encompasses a family of systems (U (t), H). For each, we obtain a
detailed spectral representation, and we compute the scattering operator, and
scattering matrix. We illustrate our results in the Lax-Phillips model where (U
(t), H) represents an acoustic wave equation in an exterior domain; and in
quantum tunneling for dynamics of quantum states
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