Schauder decompositions and functional calculus

Schauder Decompositions and Completeness

00 It x = S QnIf» m addition, the projections Pn = £ Q,are equicontinuous, then n = 1 « = 1 (£n)^°=1 is said to be an equi-Schauder decomposition of E. It is obvious that a Schauder basis is equivalent to a Schauder decomposition in which each subspace is one-dimensional, and that it is equi-Schauder if and only if the corresponding decomposition is equi-Schauder. For more information on Schaud...

Schauder decompositions in locally convex spaces

Upper and Lower Estimates for Schauder Frames and Atomic Decompositions

We prove that a Schauder frame for any separable Banach space is shrinking if and only if it has an associated space with a shrinking basis, and that a Schauder frame for any separable Banach space is shrinking and boundedly complete if and only if it has a reflexive associated space. To obtain these results, we prove that the upper and lower estimate theorems for finite dimensional decompositi...

Lambda-Calculus and Functional Programming

ion operator; this is because [x]M is an abbreviation for a term in which M and its subterms do not occur. On the other hand, in the natural reduction for lambda-calculus, replacements inside the scope of an abstraction are extremely natural. Thus, what is now called λβ -reduction satisfies a scheme which weak reduction does not, namely (ξ): if M reduces to N, then λx.M reduces to λx.N. (The sa...

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 ...