Let F be a totally real field with ring of integers O and p be an odd prime unramified in F . Let p be a prime above p. We prove that a mod p Hilbert modular form associated to F is determined by its restriction to the partial Serre-Tate deformation space Ĝm ⊗ Op (p-rigidity). Let K/F be an imaginary quadratic CM extension such that each prime of F above p splits in K and λ a Hecke character of...

We study a generalisation of operator spaces modelled on Lp spaces, instead of Hilbert spaces, using the notion of p-complete boundedness, as studied by Pisier and Le Merdy. We show that the Figà-Talamanca-Herz Algebras Ap(G) becomes quantised Banach algebras in this framework, and that the cohomological notion of amenability of these algebras corresponds to amenability of the locally compact g...

Given a finite set {(x~, Yi)} of ordered pairs from X × Y where X, Y are Hilbert spaces over the same field, there are numerous techniques for constructing a function, f, on X to Y such that f(xi) = y¢ • However, when X, 2" have a causality structure and f must be causal then the data interpolation problem is much more complicated. In this paper two interpolation methods, namely linear interpol...

The ability of the Rigged Hilbert Space formalism to deal with continuous spectrum is demonstrated within the example of the square barrier potential. The non-square integrable solutions of the time-independent Schrödinger equation are used to define Dirac kets, which are (generalized) eigenvectors of the Hamiltonian. These Dirac kets are antilinear functionals over the space of physical wave f...

This article describes about the difference of resolution structure and size between HornSAT and CNFSAT. We can compute HornSAT by using clauses causality. Therefore we can compute proof diagram by using Log space reduction. But we must compute CNFSAT by using clauses correlation. Therefore we cannot compute proof diagram by using Log space reduction, and reduction of CNFSAT is not P-Complete.

The ability of the Rigged Hilbert Space formalism to deal with continuous spectrum is demonstrated within the example of the square barrier potential. The non-square integrable solutions of the time-independent Schrödinger equation are used to define Dirac kets, which are (generalized) eigenvectors of the Hamiltonian. These Dirac kets are antilinear functionals over the space of physical wave f...