In this paper we show the equivalence of three techniques used in image processing: local-mode finding, robust-estimation and mean-shift analysis. The computational common element in all these image operators is the spatial-tonal normalized convolution, an image operator that generalizes the bilateral filter.

In this paper, we introduce new classesB k (a, c, p, , ) and T k (a, c, p, , ) of multivalent analytic functions defined by using the Cho-Kwon-Srivastava operator. We use a strong convolution technique. Inclusion results, a radius problem and some other interesting properties of these classes are discussed.

We prove that convolution with arclength measure on the curve parametrized by h(t) := (t, t, . . . , t) is a bounded operator from L(R) to L(R) for the full conjectured range of exponents, improving on a result due to M. Christ. We also obtain nearly sharp Lorentz space bounds.

We consider the problem of separability: decide whether a Hermitian operator on a finite dimensional Hilbert tensor product H = H ⊗ · · ·⊗H is separable or entangled. We show that the tensor convolution ( φ . . . φ ) : G → H defined for mappings φ : G → H μ on an almost arbitrary locally compact abelian group G, give rise to formulation of an equivalent problem to the separability one.

We prove sharp estimates for the dilation operator f(x) 7−→ f(λx), when acting on Wiener amalgam spaces W (L, L). Scaling arguments are also used to prove the sharpness of the known convolution and pointwise relations for modulation spaces M, as well as the optimality of an estimate for the Schrödinger propagator on modulation spaces.

In this article, we use the concept of symmetric q-calculus and convolution in order to define a q-differential operator for multivalent functions. This is an extension classical Ruscheweyh differential operator. By using technique subordination, derive several interesting applications newly defined

This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...

Using convolution (or Hadamard product), we define the El-Ashwah and Drbuk linear operator, which is a multivalent function in unit disk U=w:w<1 w∈₵, satisfy its specific relationship to derive subordination, superordination, sandwich results for this operator by using properties of subordination superordination concepts.