Functionals and hardware

Equivalence of K-functionals and modulus of smoothness for fourier transform

In Hilbert space L2(Rn), we prove the equivalence between the mod-ulus of smoothness and the K-functionals constructed by the Sobolev space cor-responding to the Fourier transform. For this purpose, Using a spherical meanoperator.

Implementing functionals in HCL

Almost multiplicative linear functionals and approximate spectrum

We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...

Entropic and informatic matroids

This paper studies dependencies between random variables by means of information theoretic functionals such as the entropy and the mutual information. In particular, extremal dependencies (defined in terms of these functionals) are shown to have combinatorial structures corresponding to linear matroids. From a combinatorial point of view, this provides a characterization of a new class of matro...

Monotonicity Formulas under Rescaled Ricci Flow

In this short notes, we discuss monotonicity formulas under various rescaled versions of Ricci flow. The main result is Theorem 2.1. 1. Functionals Wek from rescaled Ricci flow point of view This is the research notes when the author wrote [Li07]. In the first section, we discuss the relation between functionals Wek(g, f, τ) and rescaled Ricci flow. In Theorem 4.2 [Li07] , we have defined funct...