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Hall's transformation via quantum stochastic calculus

Paula Cohen, Robin Hudson, K. Parthasarathy, Sylvia Pulmannová (1998)

Banach Center Publications

It is well known that Hall's transformation factorizes into a composition of two isometric maps to and from a certain completion of the dual of the universal enveloping algebra of the Lie algebra of the initial Lie group. In this paper this fact will be demonstrated by exhibiting each of the maps in turn as the composition of two isometries. For the first map we use classical stochastic calculus, and in particular a stochastic analogue of the Dyson perturbation expansion. For the second map we make...

Hankel multipliers and transplantation operators

Krzysztof Stempak, Walter Trebels (1997)

Studia Mathematica

Connections between Hankel transforms of different order for L p -functions are examined. Well known are the results of Guy [Guy] and Schindler [Sch]. Further relations result from projection formulae for Bessel functions of different order. Consequences for Hankel multipliers are exhibited and implications for radial Fourier multipliers on Euclidean spaces of different dimensions indicated.

Hankel Transform in Quantum Calculus and Applications

Haddad, Meniar (2006)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 44A15, 33D15, 81Q99This paper is devoted to study the q-Hankel transform associated with the third q-Bessel function called also Hahn-Exton function. We use the q- approximation of unit for establishing a q-inverse formula of this transform. Moreover, we establish the related q-Parseval theorem.

Hankel type integral transforms connected with the hyper-Bessel differential operators

Yurii Luchko, Virginia Kiryakova (2000)

Banach Center Publications

In this paper we give a solution of a problem posed by the second author in her book, namely, to find symmetrical integral transforms of Fourier type, generalizing the cos-Fourier (sin-Fourier) transform and the Hankel transform, and suitable for dealing with the hyper-Bessel differential operators of order m>1 B : = x - β ∏ j = 1 m ( x ( d / d x ) + β γ j ) , β>0, γ j ∈ R , j=1,...,m. We obtain such integral transforms corresponding to hyper-Bessel operators of even order 2m and belonging to the class of the Mellin convolution type transforms...

Heat kernels and Riesz transforms on nilpotent Lie groups

A. ter Elst, Derek Robinson, Adam Sikora (1998)

Colloquium Mathematicae

We consider pure mth order subcoercive operators with complex coefficients acting on a connected nilpotent Lie group. We derive Gaussian bounds with the correct small time singularity and the optimal large time asymptotic behaviour on the heat kernel and all its derivatives, both right and left. Further we prove that the Riesz transforms of all orders are bounded on the Lp -spaces with p ∈ (1, ∞). Finally, for second-order operators with real coefficients we derive matching Gaussian lower bounds...

Herz-Type Hardy Spaces for the Dunkl Operator on the Real Line

Gasmi, A., Sifi, M., Soltani, F. (2006)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: Primary 46F12, Secondary 44A15, 44A35We introduce some new weighted Herz spaces associated with the Dunkl operator on R. Also we characterize by atomic decompositions the corresponding Herz-type Hardy spaces. As applications we investigate the Dunkl transform on these spaces and establish a version of Hardy inequality for this transform.* The authors are supported by the DGRST research project 04/UR/15-02.

Hilbert transform and singular integrals on the spaces of tempered ultradistributions

Andrzej Kamiński, Dušanka Perišić, Stevan Pilipović (2000)

Banach Center Publications

The Hilbert transform on the spaces S ' * ( R d ) of tempered ultradistributions is defined, uniquely in the sense of hyperfunctions, as the composition of the classical Hilbert transform with the operators of multiplying and dividing a function by a certain elliptic ultrapolynomial. We show that the Hilbert transform of tempered ultradistributions defined in this way preserves important properties of the classical Hilbert transform. We also give definitions and prove properties of singular integral operators...

Hilbert transform, Toeplitz operators and Hankel operators and invariant A∞ weights.

Sergei Treil, Alexander Volberg, Dechao Zheng (1997)

Revista Matemática Iberoamericana

In this paper, several sufficient conditions for boundedness of the Hilbert transform between two weighted Lp-spaces are obtained. Invariant A∞ weights are obtained. Several characterizations of invariant A∞ weights are given. We also obtain some sufficient conditions for products of two Toeplitz operators of Hankel operators to be bounded on the Hardy space of the unit circle using Orlicz spaces and Lorentz spaces.

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