Search results for "Operator theory"

HOLOMORPHIC SUPERPOSITION OPERATORS BETWEEN BANACH FUNCTION SPACES

2013

AbstractWe prove that for a large class of Banach function spaces continuity and holomorphy of superposition operators are equivalent and that bounded superposition operators are continuous. We also use techniques from infinite dimensional holomorphy to establish the boundedness of certain superposition operators. Finally, we apply our results to the study of superposition operators on weighted spaces of holomorphic functions and the$F(p, \alpha , \beta )$spaces of Zhao. Some independent properties on these spaces are also obtained.

Dynamics, Operator Theory, and Infinite Holomorphy

2014

FREDHOLM THEORY FOR DEGENERATE PSEUDODIFFERENTIAL OPERATORS ON MANIFOLDS WITH FIBERED BOUNDARIES

2001

We consider the calculus Ψ*,* de(X, deΩ½) of double-edge pseudodifferential operators naturally associated to a compact manifold X whose boundary is the total space of a fibration. This fits into the setting of boundary fibration structures, and we discuss the corresponding geometric objects. We construct a scale of weighted double-edge Sobolev spaces on which double-edge pseudodifferential operators act as bounded operators, characterize the Fredholm elements in Ψ*,* de(X) by means of the invertibility of an appropriate symbol map, and describe a K-theoretical formula for the Fredholm index extending the Atiyah–Singer formula for closed manifolds. The algebra of operators of order (0, 0) i…

Cohomology, central extensions, and (dynamical) groups

1985

We analyze in this paper the process of group contraction which allows the transition from the Einstenian quantum dynamics to the Galilean one in terms of the cohomology of the Poincare and Galilei groups. It is shown that the cohomological constructions on both groups do not commute with the contraction process. As a result, the extension coboundaries of the Poincare group which lead to extension cocycles of the Galilei group in the “nonrelativistic” limit are characterized geometrically. Finally, the above results are applied to a quantization procedure based on a group manifold.

The length of $C^\ast $-algebras of $\mathrm {b}$-pseudodifferential operators

1999

Isometric dilations and 𝐻^{∞} calculus for bounded analytic semigroups and Ritt operators

2017

We show that any bounded analytic semigroup on L p L^p (with 1 > p > ∞ 1>p>\infty ) whose negative generator admits a bounded H ∞ ( Σ θ ) H^{\infty }(\Sigma _\theta ) functional calculus for some θ ∈ ( 0 , π 2 ) \theta \in (0,\frac {\pi }{2}) can be dilated into a bounded analytic semigroup ( R t ) t ⩾ 0 (R_t)_{t\geqslant 0} on a bigger L p L^p -space in such a way that R t R_t is a positive contraction for any t ⩾ 0 t\geqslant 0 . We also establish a discrete analogue for Ritt operators and consider the case when L p L^p -spaces are replaced by more general Banach spaces. In connection with these functional calculus issues, we study isometric dilations of bounded continuous rep…

Analysis of geometric operators on open manifolds: A groupoid approach

2001

The first five sections of this paper are a survey of algebras of pseudodifferential operators on groupoids. We thus review differentiable groupoids, the definition of pseudodifferential operators on groupoids, and some of their properties. We use then this background material to establish a few new results on these algebras, results that are useful for the analysis of geometric operators on non-compact manifolds and singular spaces. The first step is to establish that the geometric operators on groupoids are in our algebras. This then leads to criteria for the Fredholmness of geometric operators on suitable non-compact manifolds, as well as to an inductive procedure to study their essentia…

On coincidence and common fixed point theorems of eight self-maps satisfying an FM-contraction condition

2019

In this paper, a new type of contraction for several self-mappings of a metric space, called FM-contraction, is introduced. This extends the one presented for a single map by Wardowski [Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012:94, 2012]. Coincidence and common fixed point of eight self mappings satisfying FM-contraction conditions are established via common limit range property without exploiting the completeness of the space or the continuity of the involved maps. Coincidence and common fixed point of eight self-maps satisfying FM-contraction conditions via the common property (E.A.) are also studied. Our results generaliz…

Estimation of Personalized Minimal Purkinje Systems From Human Electro-Anatomical Maps

2021

The Purkinje system is a heart structure responsible for transmitting electrical impulses through the ventricles in a fast and coordinated way to trigger mechanical contraction. Estimating a patient-specific compatible Purkinje Network from an electro-anatomical map is a challenging task, that could help to improve models for electrophysiology simulations or provide aid in therapy planning, such as radiofrequency ablation. In this study, we present a methodology to inversely estimate a Purkinje network from a patient's electro-anatomical map. First, we carry out a simulation study to assess the accuracy of the method for different synthetic Purkinje network morphologies and myocardial junct…

On the stability of the localized single-valued extension property under commuting perturbations

2013

This article concerns the permanence of the single-valued extension property at a point under suitable perturbations. While this property is, in general, not preserved under sums and products of commuting operators, we obtain positive results in the case of commuting perturbations that are quasi-nilpotent, algebraic, or Riesz operators.