Oscillator Semigroup over a Non-Archimedean Field

Global Newton Iteration over Archimedean and non-Archimedean Fields

In this paper, we study iterative methods on the coefficients of the rational univariate representation (RUR) of a given algebraic set, called global Newton iteration. We compare two natural approaches to define locally quadratically convergent iterations: the first one involves Newton iteration applied to the approximate roots individually and then interpolation to find the RUR of these approx...

Kirillov Theory for Gl2( ) Where Is a Division Algebra over a Non-archimedean Local Field

The norm of the non-self-adjoint harmonic oscillator semigroup

We identify the norm of the semigroup generated by the non-selfadjoint harmonic oscillator acting on L2(R), for all complex times where it is bounded. We relate this problem to embeddings between Gaussian-weighted spaces of holomorphic functions, and we show that the same technique applies, in any dimension, to the semigroup e−tQ generated by an elliptic quadratic operator acting on L2(Rn). The...

ON NILPOTENT ORBITS OF SLn AND Sp2n OVER A LOCAL NON-ARCHIMEDEAN FIELD

We relate the partition-type parametrization of rational (arithmetic) nilpotent adjoint orbits of the classical groups SLn and Sp2n over local non-Archimedean fields with a parametrization, introduced by DeBacker in 2002, which uses the associated Bruhat-Tits building to relate the question to one over the residue field.

Semigroup Algebras of the Full Matrix Semigroup Over a Finite Field

Let M denote the multiplicative semigroup of all n-by-n matrices over a finite field F and K a commutative ring with an identity element in which the characteristic of F is a unit. It is proved here that the semigroup algebra K[M] is the direct sum of n + 1 algebras, namely, of one full matrix algebra over each of the group algebras K[GL(r, F)] with r = 0, 1, ..., n . The degree of the relevant...