Showing papers on "Kernel (image processing) published in 1973"
TL;DR: In this article, the product ϕλ(α,β), α, β, β with explicit non-negative kernel with α≧β≧−1/2.
Abstract: The product ϕλ(α,β)(t1)ϕλ(α,β)(t2) of two Jacobi functions is expressed as an integral in terms of ϕλ(α,β)(t3) with explicit non-negative kernel, when α≧β≧−1/2. The resulting convolution structure for Jacobi function expansions is studied. For special values of α and β the results are known from the theory of symmetric spaces.
178 citations
TL;DR: In this article, the separation of a smooth circular inclusion from a matrix is treated using finite integral transforms, and the problem of finding the extent of separation and the contact pressure is reduced to the solution of a Fredholm integral equation with a weakly singular kernel.
38 citations
TL;DR: In this article, the Breit-Wigner formula for the three-body system including the break-up channel is derived for the real symmetric kernel and the Faddeev amplitude is expressed in the N/D form in terms of the real reciprocal matrix K.
8 citations
TL;DR: An algebraic convolution law is dermed to replace integration; this provides an efficient digital computation algorithm that can be transformed into the algebraic manipulation of numbers by a digital computer.
Abstract: This paper describes a general systematic procedure for the convolution of functions that are piecewise polynomial. The procedure can be implemented by hand using a simple table format or programmed for execution on a digital computer. An algebraic convolution law is dermed to replace integration; this provides an efficient digital computation algorithm. Thus, convolution operations of any complexity can be transformed into the algebraic manipulation of numbers by a digital computer.
6 citations
TL;DR: In this article, a method for reducing two-dimensional stationary problems of the diffraction of short acoustic and elastic waves at obstacles of the segment type to integral equations of the second kind is described.
Abstract: A METHOD is described for reducing two-dimensional stationary problems of the diffraction of short acoustic and elastic waves at obstacles of the segment type to integral equations of the second kind. It is shown that the principle of contractive mappings is applicable to these equations when the wavelength is sufficiently short. We investigate at the same time integral equations in which the kernel depends on the absolute value of the difference between two arguments, and when the arguments vary over a finite interval, under the assumption that the Fourier transform of the kernel has a finite number of zeros and cuts in the complex plane.
5 citations
TL;DR: In this article, the authors interpreted the convolution of the unknown spectrum with a kernel depending on the instrument and data reduction characteristics, which allowed to establish the adequacy of the overall technique for spectral determination.
2 citations