Bilinear forms on the Dirichlet space

Bilinear Forms on the Dirichlet Space

Hankel operators on the Hardy space of the disk, H (D) , can be studied as linear operators from H (D) to its dual space, as conjugate linear operators from H (D) to itself, or, in the viewpoint we will take here, as bilinear functionals on H (D) × H (D) . In that formulation, given a holomorphic symbol function b we consider the bilinear Hankel form, defined initially for f, g in P (D) , the s...

A note on bilinear forms

Bilinear Forms on Frobenius Algebras

We analyze the homothety types of associative bilinear forms that can occur on a Hopf algebra or on a local Frobenius k-algebra R with residue field k. If R is symmetric, then there exists a unique form on R up to homothety iff R is commutative. If R is Frobenius, then we introduce a norm based on the Nakayama automorphism of R. We show that if two forms on R are homothetic, then the norm of th...

On the Complexity of Bilinear Forms∗

This paper provides some new lower and upper bounds on computing bilinear forms by arithmetic circuits. The complexity measures considered are circuit size, formula size and time-space trade-offs.

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...