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...

The bounds of eigenvalues which are independent of both degrees of high-order elements and mesh sizes are shown for the preconditioned system by bilinear elements for the highorder finite elements discretizations applied to a model uniformly elliptic operator.

In this article, we prove some weighted pointwise estimates for three discontinuous Galerkin methods with lifting operators appearing in their corresponding bilinear forms. We consider a Dirichlet problem with a general second order elliptic operator.

We are interested in approximation of a multivariate function f(x1, . . . , xd) by linear combinations of products u (x1) · · ·u(xd) of univariate functions u(xi), i = 1, . . . , d. In the case d = 2 it is the classical problem of bilinear approximation. In the case of approximation in the L2 space the bilinear approximation problem is closely related to the problem of singular value decomposit...

A completely bounded bilinear operator φ: M×M → M on a von Neumann algebra M is said to have a factorization in M if there exist completely bounded linear operators ψj , θj : M → M such that

We have developed an algebraic framework for the study of recursion. For immediate linear recursion, a Horn clause is represented by a relational algebra operator. We show that the set of all such operators forms a closed semiring. In this formalism, query answering corresponds to solving a linear equation. For the first time, we are able to have the query answer expressed in an explicit algebr...

Regular operators on L p-spaces are characterised in terms of an operator bound which is associated with certain generalisations of the Feynman-Kac formula. of multiplication by the characteristic functions of elements of the-algebra S, so that if f is a bounded S-measurable function, Q(f) = R f dQ is the operator of multiplication by f. When is it true that we can nd a positive number C such t...

X iv :m at h/ 02 10 08 4v 2 [ m at h. C A ] 1 3 D ec 2 00 2 Abstract. Recently Wolff [28] obtained a sharp L2 bilinear restriction theorem for bounded subsets of the cone in general dimension. Here we adapt the argument of Wolff to also handle subsets of “elliptic surfaces” such as paraboloids. Except for an endpoint, this answers a conjecture of Machedon and Klainerman, and also improves upon ...

A~tract, In 1956, Rankin described which polynomials in the derivatives of modular forms are again modular forms, and in 1977, H Cohen defined for each n i> 0 a bilinear operation which assigns to two modular forms f and g of weight k and l a modular form If, g], of weight k + l + 2n. In the present paper we study these "Rankin-Cohen brackets" from t w o points of view. On the one hand we give ...

In this note we characterize the compact weighted Frobenius-Perron operator $p$ on $L^1(Sigma)$ and determine their spectra. We also show that every weakly compact weighted Frobenius-Perron operator on $L^1(Sigma)$ is compact.