Results 211 to 220 of about 550,724 (243)
Some of the next articles are maybe not open access.
EQUATIONS WITH A DIFFERENCE KERNEL ON A FINITE INTERVAL
Russian Mathematical Surveys, 1980ContentsIntroduction CHAPTER 1. Invertible operators with a difference kernel § 1. Construction of the inverse operator § 2. Existence conditions and the structure of the inverse operator § 3. Equations with a special right-hand side § 4. Operators with difference kernel in the space CHAPTER 2.
openaire +2 more sources
Equations with a difference kernel on a system of intervals
Journal of Soviet Mathematics, 1990The author gives sufficient conditions for the existence of a solution of the integral equation in the space \(L^ p_ n(0,w)\) \[ (1)\quad d/dx\int^{w}_{0}S(x,t)y(t)dt=g(x), \] where \(w>0\), S(x,t) is an \(n\times n\)-matrix of the form \([K_{i,j}(w_ ix-w_ jt)]^ n_{i,j=1}\), where \(K_{i,j}\in L^ q(-w_ jw,w_ iw)\), \(w_ k>0\), \(1/p+1/q=1\).
openaire +2 more sources
Associated differential equations and their bergman kernels
Complex Variables, Theory and Application: An International Journal, 1983To each formally-hyperbolic differential equation one can associate a differential equation of the same type by means of a suitable differential operator S of first order. A necessary and sufficient condition for such an operator is derived. For special cases an explicit characterisation of S is possible. Finally we obtain a construction method for the
openaire +2 more sources
Algebraic structure and kernel of the Schrodinger equation
Journal of Physics A: Mathematical and General, 1987The author derives the kernel of the Schrödinger equation in the following special cases: free particle, harmonic oscillator, harmonic oscillator and gravitational field, uniform field. His result are deduced from the consideration of the commutation relations of the Lie algebra. It is remarked that the same results can be obtained by using the Feynman'
openaire +2 more sources
A Domain Integral Equation for the Bergman Kernel
Results in Mathematics, 1999This paper is devoted to these integral operators which have a reproducing property. The authors consider special representations of the Szegő, the Bergman and the Cauchy kernels. In generalization of Henrici's function-theoretic approach they obtained a boundary integral equation of the second-order for the Bergman kernel.
Murid, A. H. M. +2 more
openaire +1 more source
Uniqueness of Kernel Functions of the Heat Equation
Potential Analysis, 1994For \(\alpha \in \mathbb{R}\), let \(\Omega_\alpha = \{(x,t) : t < 0\), \(|x |< |t |^\alpha\}\) in \(\mathbb{R}^2\). A kernel function at infinity is a positive solution of the heat equation on \(\Omega_\alpha\), which is not identically zero but vanishes continuously on \(\partial \Omega_\alpha\).
openaire +2 more sources
On Nonlinear Volterra Equations with Nonintegrable Kernels
SIAM Journal on Mathematical Analysis, 1980In this paper, the asymptotic behavior of solutions of the nonlinear real Volterra equation \[x(t) + \int_0^t {g(x(t - s))a(s)ds = f(t),\quad t \geqq 0} \] is studied. Here a and f are given and x is the unknown function. The assumptions on the function f are rather weak, and in most cases it is assumed that $\int _0^\infty a(s)ds = + \infty $.
openaire +1 more source
Reproducing kernels and Riccati equations.
2001Summary: The purpose of this paper is to exhibit a connection between the Hermitian solutions of matrix Riccati equations and a class of finite-dimensional reproducing kernel Krein spaces. This connection is then exploited to obtain minimal factorizations of rational matrix-valued functions that are \(J\)-unitary on the imaginary axis in a natural way.
openaire +1 more source
Some integral equations with 'nonrational' kernels
IEEE Transactions on Information Theory, 1966Fredholm integral equations of the first and second kind arise in many problems in statistical communication theory. However, almost all cases in which solutions are known, for equations over finite intervals, involve covariance kernels with rational Fourier transforms.
openaire +3 more sources