A $it{weighted~slant~Toep}$-$it{Hank}$ operator $L_{phi}^{beta}$ with symbol $phiin L^{infty}(beta)$ is an operator on $L^2(beta)$ whose representing matrix consists of all even (odd) columns from a weighted slant Hankel (slant weighted Toeplitz) matrix, $beta={beta_n}_{nin mathbb{Z}}$ be a sequence of positive numbers with $beta_0=1$. A matrix characterization for an operator to be $it{weighte...

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

We present an algorithm to compute the geodesic $$L_1$$ farthest-point Voronoi diagram of m point sites in presence n rectangular obstacles plane. It takes $$O(nm+n \log + m\log m)$$ construction time using O(nm) space. This is first optimal for constructing obstacles. can construct a data structure same and space that answers farthest-neighbor query $$O(\log (n+m))$$ time.

Heyde proved that the Gaussian distribution on real line is characterized by symmetry of conditional one linear form given another. The present article devoted to a group analogue theorem. We describe distributions independent random variables $$\xi _1$$ and _2$$ with values in $$X=\mathbf {R}^n\times D$$ , where D discrete Abelian group, which are $$L_2 = \xi _1 + \delta $$L_1 $$\delta $$ topo...

Let A be a bounded linear operator on a Banach space X. We investigate the conditions of existing rank-one operator B such that I+f(A)B is invertible for every analytic function f on sigma(A). Also we compare the invariant subspaces of f(A)B and B. This work is motivated by an operator method on the Banach space ell^2 for solving some PDEs which is extended to general operator space under some ...