相关论文: General methods for constructing bispectral operat…

For a large class of integral operators or second order differential operators, their isospectral (or cospectral) operators are constructed explicitly in terms of $h$-transform (duality). This provides us a simple way to extend the known…

We introduce an algebraic multiscale method for two--dimensional problems. The method uses the generalized multiscale finite element method based on the quadrilateral nonconforming finite element spaces. Differently from the…

We define the concept of a bi-operad. We develop the homotopy theory of "Bital-Sets" and of infinite-bi-operads. We develop a geometry of generalized schemes based on the spectra of distributive monochromatic bi-operads.

We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for…

The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…

We display methods that allow for computations of spectra, pseudospectra and resolvents of linear operators on Hilbert spaces and also elements in unital Banach algebras. The paper considers two different approaches, namely, pseudospectral…

The notions of spectral measures and spectral classes, which are well known for graphs, are generalized and investigated for oriented hypergraphs.

Bilinear systems of equations are defined, motivated and analyzed for solvability. Elementary structure is mentioned and it is shown that all solutions may be obtained as rank one completions of a linear matrix polynomial derived from…

We propose a method for finding gaps in the spectrum of a differential operator. When applied to the one-dimensional Hamiltonian of the quartic oscillator, a simple algebraic algorithm is proposed that, step by step, separates with a…

A general form for ladder operators is used to construct a method to solve bound-state Schr\"odinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the…

We give a computationally efficient method for constructing the linear differential operator with polynomial coefficients whose space of holomorphic solutions is spanned by all the branches of a function defined by a generic algebraic…

We give a very brief introduction to the machinery of spectral sequences, including the spectral sequence of a bicomplex. We then briefly introduce a generalisation of the spectral sequences of a bicomplex to the spectral sequences of…

The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…

Combining the derivative operator with a binomial sum from the telescoping method, we establish a family of summation formulas involving generalized harmonic numbers.

We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…

Using the group theoretic method of spectrum generating algebras a class of differential equations is obtained whose eigenvalues are calculated without explicitly solving the equations. Solutions can be easily obtained by group theoretic…

The aim of this paper is to classify the bispectral operators of any rank with regular singular points (the infinite point is the most important one). We characterise them in several ways. Probably the most important result is that they are…

Self-adjoint operators on infinite-dimensional spaces with continuous spectra are abundant but do not possess a basis of eigenfunctions. Rather, diagonalization is achieved through spectral measures. The SpecSolve package [SIAM Rev., 63(3)…

In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…

An absolute continuity approach to quasinormality which relates the operator in question to the spectral measure of its modulus is developed. Algebraic characterizations of some classes of operators that emerged in this context are…