Catalogue Search | MBRL
Are you sure you want to remove the book from the shelf?
{{itemTitle}}
35,906
result(s) for
"Operator Theory"
Sort by:
Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory
In this paper, we study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and
operator theory. We first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the
Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. We propose a new notion of tensored-scalar singularity, and
then answer questions on Hankel operators with matrix-valued bounded type symbols. We also examine an interpolation problem related to a
certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical Hermite-Fejér
Interpolation Problem for matrix rational functions. We then extend the
eBook
Instability, index theorem, and exponential trichotomy for Linear Hamiltonian PDEs
Consider a general linear Hamiltonian system
eBook
Asymptotic Spreading for General Heterogeneous Fisher-KPP Type Equations
In this monograph, we review the theory and establish new and general results regarding spreading properties for heterogeneous
reaction-diffusion equations:
The characterizations of these sets involve two new notions of generalized principal eigenvalues
for linear parabolic operators in unbounded domains. In particular, it allows us to show that
eBook
Singular integrals in quantum Euclidean spaces
We shall establish the core of singular integral theory and pseudodifferential calculus over the archetypal algebras of
noncommutative geometry: quantum forms of Euclidean spaces and tori. Our results go beyond Connes’ pseudodifferential calculus for
rotation algebras, thanks to a new form of Calderón-Zygmund theory over these spaces which crucially incorporates nonconvolution
kernels. We deduce
eBook
Conformal Graph Directed Markov Systems on Carnot Groups
We develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped
with a sub-Riemannian metric. In particular, we develop the thermodynamic formalism and show that, under natural hypotheses, the limit
set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen’s parameter. We illustrate our results for a variety of examples
of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include
the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the
non-real classical rank one hyperbolic spaces.
eBook
Positive Gaussian Kernels also Have Gaussian Minimizers
We study lower bounds on multilinear operators with Gaussian kernels acting on Lebesgue spaces, with exponents below one. We put
forward natural conditions when the optimal constant can be computed by inspecting centered Gaussian functions only, and we give
necessary and sufficient conditions for this constant to be positive. Our work provides a counterpart to Lieb’s results on maximizers of
multilinear operators with real Gaussian kernels, also known as the multidimensional Brascamp-Lieb inequality. It unifies and extends
several inverse inequalities.
eBook
Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions
An operator C on a Hilbert space \\mathcal H dilates to an operator T on a Hilbert space \\mathcal K if there is an isometry V:\\mathcal H\\to \\mathcal K such that C= V^* TV. A main result of this paper is, for a positive integer d, the simultaneous dilation, up to a sharp factor \\vartheta (d), expressed as a ratio of \\Gamma functions for d even, of all d\\times d symmetric matrices of operator norm at most one to a collection of commuting self-adjoint contraction operators on a Hilbert space.
eBook
Operator theory on noncommutative domains
In this volume we study noncommutative domains
Each
such a domain has a universal model
Free holomorphic functions, Cauchy transforms, and Poisson transforms on noncommutative
domains
We associate with each
We introduce two numerical invariants, the curvature and
We present a commutant lifting theorem for pure
In the
particular case when
eBook