115 citations · 1.9k across the 226 of their papers we have counts for
12 papers · 2 filters
Harmonic and Anharmonic Oscillators on the Heisenberg Group
David Rottensteiner, Michael Ruzhansky
Although there is no canonical version of the harmonic oscillator on the Heisenberg group so far, we make a strong case for a particular choice of operator by using…
Heisenberg-Modulation Spaces at the Crossroads of Coorbit Theory and Decomposition Space Theory
Véronique Fischer, David Rottensteiner, Michael Ruzhansky
We show that generalised time-frequency shifts on the Heisenberg group , realised as a unitary irreducible representation of a nilpotent Lie g…
Eigenfunction expansions of ultradifferentiable functions and ultradistributions. III. Hilbert spaces and Universality
Aparajita Dasgupta, Michael Ruzhansky
In this paper we analyse the structure of the spaces of smooth type functions, generated by elements of arbitrary Hilbert spaces, as a continuation of the research in our previous…
Approximations in with convergent Fourier series
Zhirayr Avetisyan, Martin Grigoryan, Michael Ruzhansky
For a separable finite diffuse measure space and an orthonormal basis of consisting of bounded functions ,…
Hörmander condition for pseudo-multipliers associated to the harmonic oscillator
Duván Cardona, Michael Ruzhansky
In this paper we prove Hörmander-Mihlin multiplier theorems for pseudo-multipliers associated to the harmonic oscillator (also called the Hermite operator). Our approach can be ext…
Hardy-Sobolev-Rellich, Hardy-Littlewood-Sobolev and Caffarelli-Kohn-Nirenberg inequalities on general Lie groups
Michael Ruzhansky, Nurgissa Yessirkegenov
In this paper we establish a number of geometrical inequalities such as Hardy, Sobolev, Rellich, Hardy-Littlewood-Sobolev, Caffarelli-Kohn-Nirenberg, Gagliardo-Nirenberg inequaliti…