The generalized Bochner-Riesz operator SR,λ may be defined as Sf(x) = F−1 [( 1− ρ R )λ + f̂ ] (x) where ρ is an appropriate distance function and F−1 is the inverse Fourier transform. The sharp bound ‖Sf‖L4(R2×R2) ≤ C‖f‖L4(R2×R2) is shown for the distance function ρ(ξ′, ξ”) = max{|ξ′|, |ξ′′|}. This is a rough distance function corresponding to the R4 cylinder analog {(x1, x2, x3, x4) ∈ R4, x1+ x...

Let H = −d/dx + V be a Schrödinger operator on the real line, where V ∈ L ∩ L. We define the perturbed Fourier transform F for H and show that F is an isometry from the absolute continuous subspace onto L(R). This property allows us to construct a kernel formula for the spectral operator φ(H). Schrödinger operator is a central subject in the mathematical study of quantum mechanics. Consider the...

Abstract. In this work, it has been shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve time fractional generalized KdV of order 2q+1 and certain fractional PDEs. It is shown that exponential operators are an effective method for solving certain fractional linear equations with non-constant coefficients. It may be concluded that the com...

Let M^2n be a hoph hypersurfaces with parallel ricci operator and tangent to structure vector field in Sasakian space form. First, we show that structures and properties of hypersurfaces and hoph hypersurfaces in Sasakian space form. Then we study the structure of hypersurfaces and hoph hypersurfaces with a parallel ricci tensor structure and show that there are two cases. In the first case, th...

A sequence of unitary transformations is applied to the one-electron Dirac operator in an external Coulomb potential such that the resulting operator is of the form Λ+AΛ+ + Λ−AΛ− to any given order in the potential strength, where Λ+ and Λ− project onto the positive and negative spectral subspaces of the free Dirac operator. To first order, Λ+AΛ+ coincides with the Brown-Ravenhall operator. Mor...

Graph signal processing is an emerging field which aims to model processes that exist on the nodes of a network and are explained through diffusion over this structure. works have heretofore assumed knowledge graph shift operator. Our approach investigate question filtering about we only know model. To do leverage theory graphons proposed by L. Lovasz B. Szegedy. We make three key contributions...