Related papers: Irregular and multi--channel sampling of operators
System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the…
In this article, we analyse the Kantorovich type exponential sampling operators and its linear combination. We derive the Voronovskaya type theorem and its quantitative estimates for these operators in terms of an appropriate K-functional.…
We discuss an application of the transfer operator approach to the analysis of the different spectral characteristics of 1d random band matrices (correlation functions of characteristic polynomials, density of states, spectral correlation…
Due to the increasing recording capability, functional data analysis has become an important research topic. For functional data the study of outlier detection and/or the development of robust statistical procedures has started recently.…
In this paper we study shorted operators relative to two different subspaces, for bounded operators on infinite dimensional Hilbert spaces. We define two notions of complementability in the sense of Ando for operators, and study the…
We investigate spectral properties of limit-periodic Schr\"odinger operators in $\ell^2(\Z)$. Our goal is to exhibit as rich a spectral picture as possible. We regard limit-periodic potentials as generated by continuous sampling along the…
In this paper, the problem of the order of approximation for the multivariate sampling Kantorovich operators is studied. The cases of the uniform approximation for uniformly continuous and bounded functions/signals belonging to Lipschitz…
We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
In this paper, the asymptotic distributions of estimators for the regularized functional canonical correlation and variates of the population are derived. The method is based on the possibility of expressing these regularized quantities as…
This paper investigates the boundedness of a broad class of operators within the framework of generalized Morrey-Banach function spaces. This class includes multilinear operators such as multilinear $\omega$-Calder\'{o}n-Zygmund operators,…
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…
We introduce Quantum Time-Frequency Analysis, which expands the approach of Quantum Harmonic Analysis to include modulations of operators in addition to translations. This is done by a projective representation of double-phase space, and we…
In this article we consider a class of integrable operators and investigate its connections with the following theories:the spectral theory of non-self-adjoint operators, the Riemann-Hilbert problem, the canonical differential systems and…
The paper establishes an analog Whittaker-Shannon-Kotelnikov sampling theorem for unbounded non-decaying band-limited signals. An explicit interpolation formula is obtained for signals sublinear growth with rate of growth less than 1/2. At…
In many applications, the observations can be represented as a signal defined over the vertices of a graph. The analysis of such signals requires the extension of standard signal processing tools. In this work, first, we provide a class of…
We establish a H\"{o}rmander type theorem for the multilinear pseudo-differential operators, which is also a generalization of the results in \cite{MR4322619} to symbols depending on the spatial variable. Most known results for multilinear…
Let $\mathbb{P}$ be the complete metric space consisting of positive invertible operators on an infinite-dimensional Hilbert space with the Thompson metric. We introduce the notion of operator means of probability measures on $\mathbb{P}$,…
Based on Beurling's theory of balayage, we develop the theory of non-uniform sampling in the context of the theory of frames for the settings of the Short Time Fourier Transform and pseudo-differential operators. There is sufficient…
We describe a simple algorithm for sampling $n$-qubit Clifford operators uniformly at random. The algorithm outputs the Clifford operators in the form of quantum circuits with at most $5n + 2n^2$ elementary gates and a maximum depth of…