1,722,503 research outputs found
Bernoulli–Dunkl and Apostol–Euler–Dunkl polynomials with applications to series involving zeros of Bessel functions
Get PDFWe introduce Bernoulli–Dunkl and Apostol–Euler–Dunkl polynomials as generalizations of Bernoulli and Apostol–Euler polynomials, where the role of the derivative is now played by the Dunkl operator on the real line. We use them to find the sum of many different series involving the zeros of Bessel functions
On Some Inequalities in Normed Linear Spaces
No full textUpper and lower bounds for the norm of a linear combination of
vectors are given. Applications in obtaining various inequalities for the quantities
||x/||x|| - y/||y|| || and ||x/||y|| - y/||x|| ||, where x and y are nonzero
vectors, that are related to the Massera-Schäffer and the Dunkl-Williams
inequalities are also provided. Some bounds for the unweighted Čebyšev functional
are given as well
q-Analogue of the Dunkl Transform on the Real Line
No full text[[abstract]]In this paper, we consider a q-analogue of the Dunkl operator on
R, we dene and study its associated Fourier transform which is a q-
analogue of the Dunkl transform. In addition to several properties, we
establish an inversion formula and prove a Plancherel theorem for this
q-Dunkl transform. Next, we study the q-Dunkl intertwining operator
and its dual via the q-analogues of the Riemann-Liouville and Weyl
transforms. Using this dual intertwining operator, we provide a relation
between the q-Dunkl transform and the q2-analogue Fourier transform
introduced and studied in [17, 18]
Reproducing kernels for Dunkl polyharmonic polynomials
Get PDFsummary:In this paper, we compute explicitly the reproducing kernel of the space of homogeneous polynomials of degree and Dunkl polyharmonic of degree , i.e. , , where is the Dunkl Laplacian and we study the convergence of the orthogonal series of Dunkl polyharmonic homogeneous polynomials
Dunkl convolution and elliptic regularity for Dunkl operators
No full textWe discuss in which cases the Dunkl convolution of distributions, possibly
both with non-compact support, can be defined and study its analytic
properties. We prove results on the (singular-)support of Dunkl convolutions.
Based on this, we are able to prove a theorem on elliptic regularity for a
certain class of Dunkl operators, called elliptic Dunkl operators. Finally, for
the root systems of type A we consider the Dunkl-type Riesz distributions,
prove that their Dunkl convolution exists and compute their convolution
Images of some functions and functional spaces under the Dunkl-Hermite semigroup
Get PDFsummary:We propose the study of some questions related to the Dunkl-Hermite semigroup. Essentially, we characterize the images of the Dunkl-Hermite-Sobolev space, and , , under the Dunkl-Hermite semigroup. Also, we consider the image of the space of tempered distributions and we give Paley-Wiener type theorems for the transforms given by the Dunkl-Hermite semigroup
Dunkl translations, Dunkl-type space and Riesz transforms for Dunkl transform on
Get PDFIn this paper, we will give some results on the support of Dunkl translations
on compactly supported functions. Then we will define Dunkl-type space
and Riesz transforms for Dunkl transform on , and prove the
boundedness of Riesz transforms from to Dunkl-type space under
the uniform boundedness assumption of Dunkl translations. The proof and the
definition in Dunkl setting will be harder than in the classical case for the
lack of some similar properties of Dunkl translations to that of classical
translations. We will also extend the preciseness of the description of support
of Dunkl translations on characteristic functions by Gallardo and Rejeb to that
on all nonnegative radial functions in .Comment: 12 pages;accepted for publication in Functional Analysis and its
Applications after some minor revision
Inversion of the Dual Dunkl-Sonine Transform on R Using Dunkl Wavelets
Get PDFWe prove a Calderón reproducing formula for the Dunkl continuous wavelet transform on R. We apply this result to derive new inversion formulas for the dual Dunkl-Sonine integral transform.The author is grateful to the referees and editors for careful reading and useful comments
Inversion of the Dual Dunkl-Sonine Transform on R Using Dunkl Wavelets
No full textWe prove a Calderón reproducing formula for the Dunkl continuous wavelet transform on R. We apply this result to derive new inversion formulas for the dual Dunkl-Sonine integral transform.The author is grateful to the referees and editors for careful reading and useful comments
Dunkl positive denite functions
No full text[[abstract]]We introduce the notion of Dunkl positive definite and strictly positive definite functions on R^d. This done by the use of the properties of Dunkl translation. We establish the analogue of Bochner's theorem in Dunkl setting. The case of radial functions is considered. We give a sufficient condition for a function to be Dunkl strictly positive definite on R^d
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