In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad ‎et al., ‎‎[K. Maleknejad ‎and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, ‎Appl. Math. Comput.‎ (2005)]‎ to gain...

in this article, a transversely isotropic linear elastic half-space with depth wise isotropy axis of material containing a cylindrical cavity of finite length is considered to be under the effect of an arbitrary torsion force applied on the wall of the cavity. to this end, the equation of equilibrium has been written in a cylindrical coordinate system, by dividing the involved domain to two reg...

We construct canonical integral transforms, analogous to the Fourier transform, that have periods six and three. The existence of this transform is shown to arise naturally from the expectation that the Schwartz space on the real line, viewed as the Heisenberg module of Rieffel and Connes over the rotation C*-algebra, should extend to a module action over the crossed product of the latter by th...

Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD-constant of a Banach space X equals the norm of the real (or the imaginary) part of the BeurlingAhlfors singular integral operator, acting on LpX(R ) with p ∈ (1,∞). Moreover, replacing equality by a linear equivalence, this is fo...

We show that positive definite kernel functions k(x, y), if continuous and integrable along the main diagonal, coincide with kernels of positive integral operators in L2(R). Such an operator is shown to be compact; under the further assumption k(x, x) → 0 as |x| → ∞ it is also trace class and the corresponding bilinear series converges absolutely and uniformly. If k1/2(x, x) ∈ L1(R), all these ...

In this paper, we introduce a q-analogue of the P-Widder transform and give a Parseval-Goldstein type theorem. Furthermore, we evaluate the q-Laplace transform of a product of q-Bessel functions. Several special cases of our results are also pointed out.

In this paper we apply a method of spectral theory of linear operators [10] to establish relations between the support of a function f on R with properties of its image Tf under a linear operator T : R → R. The classical approach uses analytic continuation of the image Tf into some complex domain (theorems of Paley-Wiener type [4, 5, 6, 7]), and therefore, could not apply to functions whose ima...

A sampling theorem is developed to reduce integration error in matrix-vector and linear multiplexing processors that perform discrete versions of continuous linear operations. By simply filtering the operation kernel before sampling, one can perform integration-error-free processing on inputs sampled at their Nyquist rate. Example applications to Laplace and Hilbert transformation are presented.