arXiv subjects
Publications and source records attributed to Waldemar Hebisch.
We prove that for a suitable class of representations of free group tensor products are generically irreducible. In particular we prove that there exist irreducible boundary realizations with infinite dimensional fiber.
We provide a Liouville principle for integration in terms of elliptic integrals. Our methods are essentially those of Abel and Liouville changed to modern notation. We expose Lie theoretic aspect of Liouville's work.
This paper provides a Liouville principle for integration in terms of dilogarithm and partial result for polylogarithm.
We present a powerful theorem for proving the irreducibility of tempered unitary representations of the free group.
We propose a simple abstract version of Calderon--Zygmund theory, which is applicable to spaces with exponential volume growth, and then show that amenable Lie groups can be treated within this framework.
This paper provides a Liouville principle for integration in terms of exponential integrals and incomplete gamma functions.
We investigate spectral multipliers, Bochner-Riesz means and convergence of eigenfunction expansion corresponding to the Schrödinger operator with anharmonic potential ${\mathcal L}=-\frac{d^2}{dx^2}+|x|$. We show that the Bochner-Riesz profile of the operator ${\mathcal L}$ completely coincides with such profile of the harmonic oscillator ${\mathcal H}=-\frac{d^2}{dx^2}+x^2$. It is especially surprising because the Bochner-Riesz profile for the one-dimensional standard Laplace operator is known to be essentially different and the case of operators ${\mathcal H}$ and ${\mathcal L}$ resembles more the profile of multidimensional Laplace operators. Another surprising element of the main obtained result is the fact that the proof is not based on restriction type estimates and instead entirely new perspective have to be developed to obtain the critical exponent for Bochner-Riesz means convergence.
We present a software package that guesses formulae for sequences of, for example, rational numbers or rational functions, given the first few terms. We implement an algorithm due to Bernhard Beckermann and George Labahn, together with some enhancements to render our package efficient. Thus we extend and complement Christian Krattenthaler's program Rate, the parts concerned with guessing of Bruno Salvy and Paul Zimmermann's GFUN, the univariate case of Manuel Kauers' Guess.m and Manuel Kauers' and Christoph Koutschan's qGeneratingFunctions.m.