A dual relationship between generalized Abel-Gončarov bases and certain Pincherle bases

Dual Generalized Bases in Linear Topological Spaces

A characterization of L-dual frames and L-dual Riesz bases

This paper is an investigation of $L$-dual frames with respect to a function-valued inner product, the so called $L$-bracket product on $L^{2}(G)$, where G is a locally compact abelian group with a uniform lattice $L$. We show that several well known theorems for dual frames and dual Riesz bases in a Hilbert space remain valid for $L$-dual frames and $L$-dual Riesz bases in $L^{2}(G)$.

G-Frames, g-orthonormal bases and g-Riesz bases

G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.

Duality between L-bases and B-bases

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...

On Dual Canonical Bases

The dual basis of the canonical basis of the modified quantized enveloping algebra is studied, in particular for type A. The construction of a basis for the coordinate algebra of the n × n quantum matrices is appropriate for the study the multiplicative property. It is shown that this basis is invariant under multiplication by certain quantum minors including the quantum determinant. Then a bas...