Related papers: $(k, a)$-generalized Fourier transform with negati…

Let n and k be positive integers with and k < n. Then of course SU(k,1) is contained into SU(n,1). Moreover, which is less clear - but proved by Khoroshkin -, the representation theory of SU(k,1) at the generalized infinitesimal character…

We discuss a generalization of Clifford algebras known as generalized Clifford algebras (in particular, ternary Clifford algebras). In these objects, we have a fixed higher-degree form (in particular, a ternary form) instead of a quadratic…

Let $F(z)$ be a $k$-regular series in $\mathbb{Z}[[z]]$ and $b$ be an integer with $b\ge2$. Bell, Bugeaud and Coons [BelBC] proved that $F(\frac{1}{b})$ is either rational or transcendental. In [Mi], we introduce a generalized $k$-regular…

Classical Stieltjes Transform is modified in a way to generalize both Stieltjes and Fourier transforms. This transform allows to intro- duce new classes of commutative and non-commutative generalized convolutions. Key words: Stieltjes…

In this article we study the normal bundle and the deformation to the normal cone functors to get deformation Lie groupoids that allow us to construct pushforward maps in any suitable (co)homology theory for Lie groupoids (not only…

We establish two general theorems on the local properties of the absolute summability of factored Fourier series by applying a recently defined absolute summability, $\left\vert A,\alpha_{n}\right\vert _{k}$ summability, and the class…

The Special Affine Fourier Transform or the SAFT generalizes a number of well known unitary transformations as well as signal processing and optics related mathematical operations. Unlike the Fourier transform, the SAFT does not work well…

In [Adv. Math. 196 (2005) 310-345] the author introduced a new generalized function space $\mathcal U(R^k)$ which can be naturally interpreted as the Fourier transform of the space of Sato's hyperfunctions on $R^k$. It was shown that all…

The classical Cayley transform is a birational map between a quadratic matrix group and its Lie algebra, which was first discovered by Cayley in 1846. Because of its essential role in both pure and applied mathematics, the classical Cayley…

Windowing a Fourier transform is a useful tool, which gives us the similarity between the signal and time frequency signal, and it allows to get sense when/where ceratin frequencies occur in the input signal, this method is introduced by…

Let $\Delta_{k,a}$ and $\Delta_k $ be the $(k,a)$-generalized Laguerre operator and the Dunkl Laplacian operator on $\mathbb{R}^n$, respectively. The aim of this article is twofold. First, we prove a restriction theorem for the…

A combination of direct and inverse Fourier transforms on the unitary group $U(N)$ identifies normalized characters with probability measures on $N$-tuples of integers. We develop the $N\to\infty$ version of this correspondence by matching…

We prove sharp stability estimates for the Truncated Laplace Transform and Truncated Fourier Transform. The argument combines an approach recently introduced by Alaifari, Pierce and the second author for the truncated Hilbert transform with…

We introduce a modified affine Hecke algebra $\h{H}^{+}_{q\eta}({l})$ ($\h{H}_{q\eta}({l})$) which depends on two deformation parameters $q$ and $\eta$. When the parameter $\eta$ is equal to zero the algebra $\h{H}_{q\eta=0}(l)$ coincides…

We give a general expression for the normally ordered form of a function F(w(a,a*)) where w is a function of boson annihilation and creation operators satisfying [a,a*]=1. The expectation value of this expression in a coherent state becomes…

Using a key observation due to Thiemann, a generalized Wick transform is introduced to map the constraint functionals of Riemannian general relativity to those of the Lorentzian theory, including matter sources. This opens up a new avenue…

In [BS] Babson and Steingrimsson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Let $f_{\tau;r}(n)$ be the number of $1\mn3\mn2$-avoiding…

We apply techniques introduced by Clerc, Kobayashi, Orsted and Pevzner to study the degenerate principal series of Sp(n,C). An explicit description of the K-types is provided and Knapp-Stein normalised operators are realised a symplectic…

Despite being the most popular methods of data analysis, Fourier-based techniques suffer from the problem of static resolution that is currently believed to be a fundamental limitation of the Fourier Transform. Although alternative…

For each $f\!:\!\mathbb{R}\to\mathbb{C}$ that is Henstock--Kurzweil integrable on the real line, or is a distribution in the completion of the space of Henstock--Kurzweil integrable functions in the Alexiewicz norm, it is shown that the…