In this paper it is investigated how to find a matrix representation of operators on a Hilbert space H with Bessel sequences, frames and Riesz bases. In many applications these sequences are often preferable to orthonormal bases (ONBs). Therefore it is useful to extend the known method of matrix representation by using these sequences instead of ONBs for these application areas. We will give ba...

Introduction. Whittaker models have been crucial in the development of the theory of automorphic forms. Within the Langlands-Shahidi method, Whittaker models give rise to the definition of local coefficients [Sh1,Sh2], which proved critical in establishing the proof of Langlands’s conjecture relating local L–functions to Plancherel measures for generic representations [Sh3]. This, in turn, led ...

Abstract Some examples of Appell–Dunkl sequences are shown using determined operators. Specifically, whose generating functions the form $$E_{\alpha }(xt)/(1\pm t^m)$$ E α ( x t ) /</...

Light scattered by turbid tissue is known to degrade optical coherence tomography (OCT) image contrast progressively with depth. Bessel beams have been proposed as an alternative to Gaussian beams to image deeper into turbid tissue. However, studies of turbid tissue comparing the image quality for different beam types are lacking. We present such a study, using numerically simulated beams and e...

The constants A and B are called lower and upper frame bounds for the frame. We call a frame {fi}i∈I bounded, if there exists δ > 0 such that ‖fi‖ ≥ δ for all i ∈ I (the norms of the frame elements are always uniformly bounded from above [3, Proposition 4.6]), and unit norm, if ‖fi‖ = 1 for all i ∈ I. If {fi}i∈I is a frame only for its closed linear span, we call it a frame sequence. Those sequ...

We study the existence and uniqueness of solutions of SDEs describing squared Bessel particle systems in full generality. We define non-negative and non-colliding squared Bessel particle systems and we study their properties. Particle systems dissatisfying noncolliding and unicity properties are pointed out. The structure of squared Bessel particle systems is described.

Some typographical errors have been corrected. Figure 2 of this report is not complete in this version because it should contain some hand-drawn additional arcs. The reader, however, is able work out the details for herself. Abstract We construct and discuss innnite 0-1-sequences which contain 2n diierent sub-words of length n, for every n.

Orthogonal Frequency Division Multiplexing (OFDM) is a hotly researched topic, due to its high data rate and robustness to multi-path fading. As such, it has been widely adopted in wireless standards, e.g., IEEE 802.11a/g, digital audio/video broadcasting and Integrated Services Digital Broadcasting (ISDB). In the presence of doubly-selectivity in fading channels, OFDM suffers from intercarrier...