Topic
Volterra operator
About: Volterra operator is a research topic. Over the lifetime, 276 publications have been published within this topic receiving 2769 citations.
Papers published on a yearly basis
Papers
Book•
1 Jan 2000
TL;DR: Inverse problems for difference operators: inverse problem of spectral analysis for Jacobi matrices inverse problem for a difference equation with constant coefficients the problems of determining a difference operator in non-stationary statement remarks and references as mentioned in this paper.
Abstract: Chapter 1 Inverse problems for difference operators: inverse problem of spectral analysis for Jacobi matrices inverse problem for a difference equation with constant coefficients the problems of determining a difference operator in non-stationary statement remarks and references. Chapter 2 A priori estimates and the uniqueness of integro-differential equations with operator coefficients: estimates of the Carleman type and their connection with the uniqueness of solutions of inverse problems estimates for the Schrodinger equation with operator coefficients remarks and references. Chapter 3 Inverse problems for differential equations: one-dimensional inverse problem for the wave equation in linearized statement the method of transformation operators uniqueness in multidimensional inverse problems in nonstationary and spectral statements remarks and references. Chapter 4 Volterra operator equations and their applications: Volterra operator equations in scales of Banach spaces non-hyperbolic Cauchy problem for the wave equation the problem of integral geometry in a strip the inverse problem of variational calculus remarks and references. Chapter 5 Foundations of the theory of conditionally well-posed problems: conditional well-posedness lh well-posedness of difference schemes variational methods of solution of lh-stable difference schemes remarks and references. Chapter 6 Theory of stability of difference schemes: statement of the problem and the necessary conditions of finite stability basic estimates sufficient stability conditions estimates of l-stability up to the boundary convergence theorems finite stability of two-layer schemes of the canonical form conditions of stability in terms of the transition operator remarks and references.
328 citations
1 Jan 1980
TL;DR: In this paper, a systematic exposition of different methods of obtaining equations which are integrable by the inverse scattering method is presented, starting with elementary methods and concluding with the method of dressing operator families.
Abstract: The present article is devoted to a systematic exposition of different methods of obtaining equations which are integrable by the inverse scattering method. The exposition begins with elementary methods and concludes with the method of dressing operator families. Many results (this refers both to the elementary part and in particular to the method of dressing) are original and published for the first time.
207 citations
TL;DR: The boundedness and compactness of the products of Volterra type operators and composition operators from the space of bounded analytic functions and the Bloch space to the Zygmund space are discussed in this paper.
150 citations
124 citations
TL;DR: In this article, a unified framework for nonlinear (and, in particular, linear) system and signal analysis is presented, whereby a number of problems involving approximation and inversion of nonlinear functions, nonlinear functionals, and nonlinear operators, are cast in a reproducing kernel Hilbert space (RKHS) setting, and solved by orthogonal projection methods.
Abstract: A unified framework is presented for nonlinear (and, in particular, linear) system and signal analysis, whereby a number of problems involving approximation and inversion of nonlinear functions, nonlinear functionals, and nonlinear operators, are cast in a reproducing kernel Hilbert space (RKHS) setting, and solved by orthogonal projection methods. The RKHS's used for the above purpose are the "arbitrarily weighted Fock spaces" introduced by de Figueiredo and Dwyer in II] and called in the present paper "generalized Fock (GF) spaces". These spaces consist of polynomials or power series in one or more scalar variables, or of finite (polynomic case) or infinite Volterra functional series in one or more functions, or of finite or infinite Volterra operator series in one or more functions. In each case, the space is equipped with an appropriate weighted inner product, with the option of making the choice of weights depend on the particular problem under consideration. These developments are illustrated by means of various applications, in particular, the modeling of semiconductor device characteristics, best approximation of nonlinear systems, and cancellation of large nonlinear distortion in signals propagating through electronic equipment.
105 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 1 |
| 2021 | 13 |
| 2020 | 13 |
| 2019 | 16 |
| 2018 | 23 |
| 2017 | 11 |