Closed operator functional calculus in Banach modules and applications

Functional Itô calculus and Applications

Functional Itô calculus and Applications David-Antoine FOURNIE This thesis studies extensions of the Itô calculus to a functional setting, using analytical andprobabilistic methods, and applications to the pricing and hedging of derivative securities. The first chapter develops a non-anticipative pathwise calculus for functionals of twocadlag paths, with a predictable dependence in the ...

On the Cauchy Functional Inequality in Banach Modules

Operator Representations of Function Algebras and Functional Calculus

This paper deals with some operator representations Φ of a weak*-Dirichlet algebra A, which can be extended to the Hardy spaces H(m), associated to A and to a representing measure m of A, for 1 ≤ p ≤ ∞. A characterization for the existence of an extension Φp of Φ to L(m) is given in the terms of a semispectral measure FΦ of Φ. For the case when the closure in L(m) of the kernel in A of m is a s...

Holomorphic Functional Calculus and Some Applications

In this note, we present some applications of complex analysis to functional analysis and operator theory. We will focus on some basic facts of holomorphic functional calculus and its applications to analyze the spectrum of operators.

Approximate mixed additive and quadratic functional in 2-Banach spaces

In the paper we establish the general solution of the function equation f(2x+y)+f(2x-y) = f(x+y)+f(x-y)+2f(2x)-2f(x) and investigate the Hyers-Ulam-Rassias stability of this equation in 2-Banach spaces.