In this study, we present the Catalan transforms of k-Pell sequence, k-Pell–Lucas sequence and Modified examine properties sequences. Then apply Hankel transform to sequence. Also, obtain generating functions Furthermore, acquire an interesting characteristic related determinant

in hilbert space l2(rn), we prove the equivalence between the mod-ulus of smoothness and the k-functionals constructed by the sobolev space cor-responding to the fourier transform. for this purpose, using a spherical meanoperator.

We develop an analytic approach to the Radon transform f̂(ζ) = ∫ τ⊂ζ f(τ), where f(τ) is a function on the affine Grassmann manifold G(n, k) of k-dimensional planes in Rn, and ζ is a k′-dimensional plane in the similar manifold G(n, k′), k′ > k. For f ∈ Lp(G(n, k)), we prove that this transform is finite almost everywhere on G(n, k′) if and only if 1 ≤ p < (n− k)/(k′− k), and obtain explicit inv...

The Radon transform constitutes a fundamental concept for x-rays in medical imaging, and more generally, in image reconstruction problems from diverse fields. The Radon transform in Euclidean spaces assigns to functions their integrals over affine hyperplanes. This can be extended so that the integration is performed on affine k-dimensional subspaces, the corresponding transform is called k-pla...

and Applied Analysis 3 3. Two-Dimensional Differential Transform Method The two-dimensional differential transform of function w(x, y) is defined as W(k, h) = 1 k!h! [ ∂ k+h w (x, y) ∂x∂y ] x=0 y=0 , (9) where it is noted that upper case symbol W(k, h) is used to denote the two-dimensional differential transform of a function represented by a corresponding lower case symbol w(x, y). The differe...

This paper presents a computationally efficient technique for decomposing non-orthogonally superposed $k$ geometric sequences. The method, which is named as sequence decomposition with $k$-simplexes transform (GSD-ST), based on the concept of transforming an observed to multiple in virtual $k$-dimensional space and correlating volumes transformed simplexes. Hence, GSD-ST turns problem sequences...