Related papers: On the formula of regularized traces
We extend to manifolds endowed with a general geometric structure, the classical notions of gradient as well as Laplace operator, and provide some of their natural properties.
The method of this paper is my original creation. A new method for solving linear differential equations is proposed in this paper. The important conclusion of this paper is that arbitrary order linear ordinary differential equations with…
We present a method for the explicit diagonalization of some Hankel operators. This method allows us to recover classical results on the diagonalization of Hankel operators with the absolutely continuous spectrum. It leads also to new…
Replacing operators with continuous operator-valued functions, we prove time-dependent versions of well-known results on compressions and diagonals of bounded operators. The setting of smooth functions is also addressed. Our results have no…
In their work on differential operators in positive characteristic, Smith and Van den Bergh define and study the derived functors of differential operators; they arise naturally as obstructions to differential operators reducing to positive…
In this work we deduce explicit formulae for the elements of the matrices that represent the action of integro-differential operators over the coefficients of generalized Fourier series. Our formulae are obtained by performing operations on…
In this paper we study a class of Jacobi operators, such that each operator is generated by the unit Borel measure with a support consisting of a finite number of intervals on the real line R and a finite number of points in C, located…
We consider the problem of approaching real numbers with rational numbers with prime denominator and with a single numerator allowed for each denominator. We then present a simple application, related to possible correlations between trace…
We present analytic formulae that simplify the evaluation of the normalization of continuous spectrum stationary states in the one-dimensional Schr\"odinger equation.
We introduce and systematically develop two classes of discrete integrable operators: those with $2\times 2$ matrix kernels and those possessing general differential kernels, thereby generalizing the discrete analogue previously studied. A…
We present a formula for the trace of any symmetric power of a $n\times n$ matrix (with coefficients in a field) in terms of the ordinary powers of the matrix, an arbitrarily chosen linear function which vanishes on the identity matrix, and…
In this short note we discuss ordinary differential equations which linearize upon one (or more) differentiations. Although the subject is fairly elementary, equations of this type arise naturally in the context of integrable systems.
For perturbed ordinally differential equations, a procedure of renormalization group method is proposed. To uniquely obtain renormalized solutions for given initial conditions, the procedure assumes that the extra integral constants yielded…
We explain how a slight variant in the use of our recursive algorithm leads to improve the known lower bounds for the absolute trace of a totally positive algebraic integer. We also link the absolute trace of a totally positive algebraic…
We characterize the trace class membership of Toeplitz operators with distributional symbols acting on the Bergman space on the unit disk. The Berezin transform of distributions, introduced in the paper, yields a formula for the trace.…
Green's formulas for elliptic cone differential operators are established. This is done by an accurate description of the maximal domain of an elliptic cone differential operator and its formal adjoint, thereby utilizing the concept of a…
In this paper, a simple and unified method is developed that predicts the relativistic alterations of physical measures when the behavior of a natural system is characterized by means of a specific operator equation. Separation of variables…
We consider the operator algebra $\mathscr A$ on $\mathscr S(\mathbb R^n)$ generated by the Shubin type pseudodifferential operators, the Heisenberg-Weyl operators and the lifts of the unitary operators on $\mathbb C^n$ to metaplectic…
A unified and systematic scheme for constraction of differential opreator realization of any irreducible representation of $sl(n)$ is developed. The $q$-analogue of this unified scheme is used to constract $q$-difference operator…
We characterize the solution to the entropically regularized optimal transport problem by a well-posed ordinary differential equation (ODE). Our approach works for discrete marginals and general cost functions, and in addition to two…