Related papers: Selected aspects of tractability analysis
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
When a solution to an abstract inverse linear problem on Hilbert space is approximable by finite linear combinations of vectors from the cyclic subspace associated with the datum and with the linear operator of the problem, the solution is…
We offer a spectral analysis for a class of transfer operators. These transfer operators arise for a wide range of stochastic processes, ranging from random walks on infinite graphs to the processes that govern signals and recursive wavelet…
We present a survey of past research activities and current results in constructing a mathematical framework describing the principle of local reflexivity for operator ideals and reveal further applications involving operator ideal products…
This is the first part of a work devoted to the study of linear Mahler systems in several variables from the perspective of transcendence and algebraic independence. We prove two main results concerning systems that are regular singular at…
Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…
When observations are curves over some natural time interval, the field of functional data analysis comes into play. Functional linear processes account for temporal dependence in the data. The prediction problem for functional linear…
The existence theory is developed for solutions of the inhomogeneous linearized field equations for causal variational principles. These equations are formulated weakly with an integral operator which is shown to be bounded and symmetric on…
In the present paper and its sequel "A unified approach to three themes in harmonic analysis ($2^{nd}$ part)", we address three rich historical themes in harmonic analysis that rely fundamentally on the concept of non-zero curvature.…
This article generalises the concept of realised covariation to Hilbert-space-valued stochastic processes. More precisely, based on high-frequency functional data, we construct an estimator of the trace-class operator-valued integrated…
We study the approximation of high-dimensional rank one tensors using point evaluations and consider deterministic as well as randomized algorithms. We prove that for certain parameters (smoothness and norm of the $r$th derivative) this…
In this article, we study the relationship between the exponential dichotomy properties of a triangular system of linear difference equations and its associated diagonal system on Hilbert spaces. We stress that all previous results in this…
This paper is devoted to the study of controllability of linear systems on generalized Heisenberg groups. Some general necessary controllability conditions and some sufficient ones are provided. We introduce the notion of decoupled systems,…
Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a…
Partial inverse problems are studied for Sturm-Liouville operators with a discontinuity. The main results of the paper are local solvability and stability of the considered inverse problems. Our approach is based on a constructive algorithm…
Parametric entities appear in many contexts, be it in optimisation, control, modelling of random quantities, or uncertainty quantification. These are all fields where reduced order models (ROMs) have a place to alleviate the computational…
In this article, we investigate certain theoretical aspects of the hierarchical controllability problem in one-dimensional wave equations within a moving domain using Stackelberg strategy. The controls are applied along a portion of the…
We study expansions of Hilbert spaces with a bounded normal operator $T$. We axiomatize this theory in a natural language and identify all of its completions. We prove the definability of the adjoint $T^*$ and prove quantifier elimination…
This work examines the Conditional Approval Framework for elections involving multiple interdependent issues, specifically focusing on the Conditional Minisum Approval Voting Rule. We first conduct a detailed analysis of the computational…