Related papers: Decomposing numerical ranges along with spectral s…
We prove bounds for a class of unital homomorphisms arising in the study of spectral sets, by involving extremal functions and vectors. These are used to recover three celebrated results on spectral constants by Crouzeix--Palencia,…
In this article, we present a space-frequency theory for spherical harmonics based on the spectral decomposition of a particular space-frequency operator. The presented theory is closely linked to the theory of ultraspherical polynomials on…
We investigate both theoretical and computational aspects of using wavelet bases to decouple physics on different scales in quantum field theory.
Decomposing an algebraic variety into irreducible or equidimensional components is a fundamental task in classical algebraic geometry and has various applications in modern geometry engineering. Several researchers studied the problem and…
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…
Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…
The purpose of this paper is to continue studying the properties of $\gamma$-regular open sets introduced and explored in [6]. The concept of $\gamma$-closed spaces have also been defined and discussed.
Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…
A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
The geometric Langlands program is distinguished in assigning spectral decompositions to all representations, not only the irreducible ones. However, it is not even clear what is meant by a spectral decomposition when one works with…
We extend the proof in [M.~Crouzeix and C.~Palencia, {\em The numerical range is a $(1 + \sqrt{2})$-spectral set}, SIAM Jour.~Matrix Anal.~Appl., 38 (2017), pp.~649-655] to show that other regions in the complex plane are $K$-spectral sets.…
This paper provides a comprehensive review of recent advancements in k-mer-based data structures representing collections of several samples (sometimes called colored de Bruijn graphs) and their applications in large-scale sequence indexing…
In this paper we are interested in spectral decomposition of an unbounded operator with discrete spectrum. We show that if $A$ generates a polynomially bounded $n$-times integrated group whose spectrum set $\sigma(A)=\{i\lambda_k;…
The useful dynamic range of an image in the diffraction limited regime is usually limited by speckles caused by residual phase errors in the optical system forming the image. The technique of speckle decorrelation involves introducing many…
In this paper, we design and analyze a novel spectral method for the subdiffusion equation. As it has been known, the solutions of this equation are usually singular near the initial time. Consequently, direct application of the traditional…
In order to treat multiplicative phenomena in twisted (co)homology, we introduce a new point-set level framework for parametrized homotopy theory. We provide a convolution smash product that descends to the corresponding…
Nuclear magnetic resonance (NMR) spectroscopy has become a formidable tool for biochemistry and medicine. Although J-coupling carries essential structural information it may also limit the spectral resolution. Homonuclear decoupling remains…
When employing non-linear methods to characterise complex systems, it is important to determine to what extent they are capturing genuine non-linear phenomena that could not be assessed by simpler spectral methods. Specifically, we are…
This work concerns a detailed review of data analysis methods used for remotely sensed images of large areas of the Earth and of other solid astronomical objects. In detail, it focuses on the problem of inferring the materials that cover…