Bilinear wavelet representation of Calderón–Zygmund forms

Bilinear Forms

The geometry of Rn is controlled algebraically by the dot product. We will abstract the dot product on Rn to a bilinear form on a vector space and study algebraic and geometric notions related to bilinear forms (especially the concept of orthogonality in all its manifestations: orthogonal vectors, orthogonal subspaces, and orthogonal bases). Section 1 defines a bilinear form on a vector space a...

Arens regularity of bilinear forms and unital Banach module spaces

Assume that $A$‎, ‎$B$ are Banach algebras and that $m:Atimes Brightarrow B$‎, ‎$m^prime:Atimes Arightarrow B$ are bounded bilinear mappings‎. ‎We study the relationships between Arens regularity of $m$‎, ‎$m^prime$ and the Banach algebras $A$‎, ‎$B$‎. ‎For a Banach $A‎$‎-bimodule $B$‎, ‎we show that $B$ factors with respect to $A$ if and only if $B^{**}$ is unital as an $A^{**}‎$‎-module‎. ‎Le...

A multivalued image wavelet representation based on multiscale fundamental forms

In this paper, a new wavelet representation for multivalued images is presented. The idea for this representation is based on the first fundamental form that provides a local measure for the contrast of a multivalued image. In this paper, this concept is extended toward multiscale fundamental forms using the dyadic wavelet transform of Mallat. The multiscale fundamental forms provide a local me...

Multiscale Fundamental Forms: A Multimodal Image Wavelet Representation

In this paper, a new wavelet representation for multimodal images is presented. The idea for this representation is based on the first fundamental form that provides a local measure for the contrast of a multimodal image. In this paper, this concept is extended towards multiscale fundamental forms using the dyadic wavelet transform of Mallat. The multiscale fundamental forms provide a local mea...

A note on bilinear forms