相关论文: About a resolvent formula

Let $T$ be a bounded linear operator on a Banach space and $f$ an analytic function, defined on the spectrum of $T$. We discuss the relations between the rate of growth of the resolvent of $T$ and of $f(T)$.

For $a,\alpha>0$ let $E(a,\alpha)$ be the set of all compact operators $A$ on a separable Hilbert space such that $s_n(A)=O(\exp(-an^\alpha))$, where $s_n(A)$ denotes the $n$-th singular number of $A$. We provide upper bounds for the norm…

We give an explicit determinant formula for a class of rational solutions of the Painlev\'e V equation in terms of the universal characters.

We prove exact formulas for weighted $2k$th moments of the Riemann zeta function for all integer $k\geq 1$ in terms of the analytic continuation of an auto-correlation function. This latter enjoys several functional equations. One of them,…

This is an English translation of "The Resolvent Problem" by Tschebotarow/Chebotarev. In this article, Chebotarev summarizes the history of the resolvent problem from compass and ruler constructions to Klein and Hilbert' formlutions of the…

We develop a unified method to study spectral determinants for several different manifolds, including spheres and hemispheres, and projective spaces. This is a direct consequence of an approach based on deriving recursion relations for the…

Extencion of Krein's special method for solving of integral equation to that method for solving of systems of integral equations is established. Generalizations of formulae for solution of integral equations are obtained. The result…

In this paper the notion of quantum finite one-counter automata (QF1CA) is introduced. Introduction of the notion is similar to that of the 2-way quantum finite state automata by A.Kondacs and J.Watrous. The well-formedness conditions for…

We study the quantum Hamiltonian reduction for affine superalgebras in the twisted case. This leads to a general representation theory of all superconformal algebras, including the twisted ones (like the Ramond algebra). In particular, we…

In this work, we develop a systematic framework for computing the resolvent of the sum of two or more monotone operators which only activates each operator in the sum individually. The key tool in the development of this framework is the…

We present formulas for the homogenous multivariate resultant as a quotient of two determinants. They extend classical Macaulay formulas, and involve matrices of considerably smaller size, whose non zero entries include coefficients of the…

We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms. These atoms are identified with the extreme points and…

Solving of regular equations via Arden's Lemma is folklore knowledge. We first give a concise algorithmic specification of all elementary solving steps. We then discuss a computational interpretation of solving in terms of coercions that…

In one of his papers, the author introduces the class of Farkas-related vectors for which a version of Farkas' lemma over integers is derived. In this paper, two similar classes are introduced and studied.

We offer a proof of a summation formula equivalent to one due to Berndt. Our proof uses the M$\ddot{u}$ntz formula and the Poisson summation formula. By utilizing known properties of Mellin inversion, we give an example from a discontinuous…

We compute two parametric determinants in which rows and columns are indexed by compositions, where in one determinant the entries are products of binomial coefficients, while in the other the entries are products of powers. These results…

This note provides formula for determinant and inverse of r-circulant matrices with general sequences of third order. In other words, the study combines many papers in the literature.

In this paper we introduce a class of mathematical objects called \emph{extensors} and develop some aspects of their theory with considerable detail. We give special names to several particular but important cases of extensors. The…

It is well-known that the equations for a simple fluid can be cast into what is called their Lagrange formulation. We introduce a notion of a generalized Lagrange formulation, which is applicable to a wide variety of systems of partial…

A new matrix operation based on inserting columns and rows, similarly to the mediant operation between fractions, gives rise to the Farey determinants matrix or, equivalently, the matrix of the numerators of the differences of Farey…