Related papers: Regular operator mappings and multivariate geometr…
We develop elements of a general dilation theory for operator-valued measures and bounded linear maps between operator algebras that are not necessarily completely-bounded. We prove our main results by extending and generalizing some known…
A quantal system in an eigenstate, of operators with a continuous nondegenerate eigenvalue spectrum, slowly transported round a circuit C by varing parameters in its Hamiltonian, will acquire a generalized geometrical phase factor. An…
We consider the Neumann version of the spherical mean value operator and its variants in the space of smooth functions, distributions and compactly supported ones. Surjectivity and range characterization issues are addressed from the…
The paper concerns a new method to obtain a direct proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the unification and refinement of several methods developed somehow separately in…
A generalised notion of geometric phase for pure states is proposed and its physical manifestations are shown. An appreciation of fact that the interference phenomenon also manifests in the average of an observable, allows us to define the…
Cumulant mapping employs a statistical reconstruction of the whole by sampling its parts. The theory developed in this work formalises and extends ad hoc methods of `multi-fold' or `multi-dimensional' covariance mapping. Explicit formulae…
We consider generic i.e., forming an everywhere dense massive subset classes of Markov operators in the space $L^2(X,\mu)$ with a finite continuous measure. Since there is a canonical correspondence that associates with each Markov operator…
The seminal work of Kubo and Ando from 1980 provided us with an axiomatic approach to means of positive operators. As most of their axioms are algebraic in nature, this approach has a clear algebraic flavor. On the other hand, it is highly…
Several algebro-geometric properties of commutative rings of partial differential operators as well as several geometric constructions are investigated. In particular, we show how to associate a geometric data by a commutative ring of…
The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.
The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometric interpretation to the concept of certainty equivalent.…
Prior knowledge on properties of a target model often come as discrete or combinatorial descriptions. This work provides a unified computational framework for defining norms that promote such structures. More specifically, we develop…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
The analysis of curves has been routinely dealt with using tools from functional data analysis. However its extension to multi-dimensional curves poses a new challenge due to its inherent geometric features that are difficult to capture…
Any procedure applied to data, and any quantity derived from data, is required to respect the nature and symmetries of the data. This axiom applies to refinement procedures and multiresolution transforms as well as to more basic operations…
We introduce a novel approach to measure the behavior of a geometric operator before and after coarsening. By comparing eigenvectors of the input operator and its coarsened counterpart, we can quantitatively and visually analyze how well…
This article extends the study of the dynamical properties of the symmetric McMillan map, emphasizing its utility in understanding and modeling complex nonlinear systems. Although the map features six parameters, we demonstrate that only…
In this paper we introduce the limit, unique solution of the nonlinear equations, geodesic property, tolerance relations and pinch on the spectral geometric mean for two positive definite operators. We show that the spectral geometric mean…
We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for…
We develop a Koopman operator framework for studying the {computational properties} of dynamical systems. Specifically, we show that the resolvent of the Koopman operator provides a natural abstraction of halting, yielding a ``Koopman…