12 citations · 18 across the 8 of their papers we have counts for
10 papers · 1 filter
Deformations and Balian-Low theorems for Gabor frames on the adeles
Ulrik Enstad, Mads S. Jakobsen, Franz Luef +1
We generalize Feichtinger and Kaiblinger's theorem on linear deformations of uniform Gabor frames to the setting of a locally compact abelian group . More precisely, we show tha…
Distribution Theory by Riemann Integrals
Hans G. Feichtinger, Mads S. Jakobsen
It is the purpose of this article to outline a course that can be given to engineers looking for an understandable mathematical description of the foundations of distribution theor…
Time-frequency analysis on the adeles over the rationals
Ulrik B. R. Enstad, Mads S. Jakobsen, Franz Luef
We show that the construction of Gabor frames in with generators in and with respect to time-frequency shifts from a rectangular la…
The inner kernel theorem for a certain Segal algebra
Mads S. Jakobsen, Hans G. Feichtinger
The Segal algebra is well defined for arbitrary locally compact Abelian Hausdorff (LCA) groups . It is a Banach space that exhibits a kernel theorem similar…
Duality of Gabor frames and Heisenberg modules
Mads S. Jakobsen, Franz Luef
Given a locally compact abelian group and a closed subgroup in , Rieffel associated to a Hilbert -module , known as a Heisenberg m…
On Wilson bases in L2(R^d)
Marcin Bownik, Mads Sielemann Jakobsen, Jakob Lemvig +1
A Wilson system is a collection of finite linear combinations of time frequency shifts of a square integrable function. In this paper we use the fact that a Wilson system is a shif…
On a (no longer) new Segal algebra - a review of the Feichtinger algebra
Mads Sielemann Jakobsen
Since its invention in 1979, the Feichtinger algebra has become a very useful Banach space of functions with applications in time-frequency analysis, the theory of pseudo-different…
Density and duality theorems for regular Gabor frames
Mads Sielemann Jakobsen, Jakob Lemvig
We investigate Gabor frames on locally compact abelian groups with time-frequency shifts along non-separable, closed subgroups of the phase space. Density theorems in Gabor analysi…
Co-compact Gabor systems on locally compact abelian groups
Mads Sielemann Jakobsen, Jakob Lemvig
In this work we extend classical structure and duality results in Gabor analysis on the euclidean space to the setting of second countable locally compact abelian (LCA) groups. We…
Reproducing formulas for generalized translation invariant systems on locally compact abelian groups
Mads Sielemann Jakobsen, Jakob Lemvig
In this paper we connect the well established discrete frame theory of generalized shift invariant systems to a continuous frame theory. To do so, we let , , be a cou…