This paper deals with continuous frames and continuous Riesz bases. We introduce continuous Riesz bases and give some equivalent conditions for a continuous frame to be a continuous Riesz basis. It is certainly possible for a continuous frame to have only one dual. Such a continuous frame is called a Riesz-type frame [13]. We show that a continuous frame is Riesz-type if and only if it is a con...

In this paper we proved that every g-Riesz basis for Hilbert space $H$ with respect to $K$ by adding a condition is a Riesz basis for Hilbert $B(K)$-module $B(H,K)$. This is an extension of [A. Askarizadeh, M. A. Dehghan, {em G-frames as special frames}, Turk. J. Math., 35, (2011) 1-11]. Also, we derived similar results for g-orthonormal and orthogonal bases. Some relationships between dual fra...

Let X ←−fZ −→gY be a correspondence of complex manifolds. We study integral transforms associated to kernels exp(φ), with φ meromor-phic on Z, acting on formal or moderate cohomologies. Our main applicationis the Laplace transform. In this case, X is the projective compactification ofthe vector space V ' Cn, Y is its dual space, Z = X×Y and φ(z, w) = 〈z,w〉.We obt...

Recent work of Pickett has given a construction of self-dual normal bases for extensions of finite fields, whenever they exist. In this article we present these results in an explicit and constructive manner and apply them, through computer search, to identify the lowest complexity of selfdual normal bases for extensions of low degree. Comparisons to similar searches amongst normal bases show t...

Abstract This article sketches a new analysis of the diachronic development found in many West Germanic languages from hybrid VO-OV order to rigid OV or VO order. The discussion departs discussions Struik & Van Kemenade ( 2020 / 2022 ) and Schoenmakers (to appear) on English/Dutch, which focus role object shift information structure. My interpretation their data will be based an earlier Bro...

abstract L-bases and B-bases are two important classes of polynomial bases used for representing surfaces in CAGD. The B ezier and multinomial bases are special cases of both L-bases and B-bases. We establish that certain proper subclasses of bivariate Lagrange and Newton bases are L-bases and certain proper subclasses of power and Newton dual bases are B-bases. A geometric point-line duality b...

We propose pivot methods that solve linear programs by trying to close the duality gap from both ends. The first method maintains a set B of at most three bases, each of a different type, in each iteration: a primal feasible basis Bp, a dual feasible basis Bd and a primal-and-dual infeasible basis Bi. From each B ∈ B, it evaluates the primal and dual feasibility of all primal and dual pivots to...