Results 221 to 230 of about 1,629 (250)

EQUATIONS WITH A DIFFERENCE KERNEL ON A FINITE INTERVAL

Russian Mathematical Surveys, 1980
ContentsIntroduction 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.
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Effect of the constant kernel in the Salpeter equation

Physical Review D, 1991
A constant scalar kernel in the Salpeter equation has the effect of reducing the mass of quarkonium in the region of {l angle}{ital p}{r angle}/{ital m} greater than 1. This effect has no {ital J} dependence, and is common to all the states. For the realistic potential including this kernel, {ital m}{sub {pi}} becomes small faster than any other meson ...
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A Domain Integral Equation for the Bergman Kernel

Results in Mathematics, 1999
This 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., Nashed, M. Z., Razali, M. R. M.   +2 more
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Algebraic structure and kernel of the Schrodinger equation

Journal of Physics A: Mathematical and General, 1987
The 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'
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On Nonlinear Volterra Equations with Nonintegrable Kernels

SIAM Journal on Mathematical Analysis, 1980
In 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 $.
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Uniqueness of Kernel Functions of the Heat Equation

Potential Analysis, 1994
For \(\alpha \in \mathbb{R}\), 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 \(\partial \Omega_\alpha\).
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Some integral equations with 'nonrational' kernels

IEEE Transactions on Information Theory, 1966
Fredholm 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.
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Reproducing kernels and Riccati equations.

2001
Summary: 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.
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Kernel Equating

2017
Jorge González, Marie Wiberg
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The Pricing Kernel Equation

SSRN Electronic Journal, 2019
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