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In the present article, we studied the properties of the Hartley transform for integrable Boehmian and proved its inversion. [ABSTRACT FROM AUTHOR]

Formulas of derivatives of the Legendre functions [image omitted] and [image omitted] with respect to μ and ν at μ, ν=0,±1,±2, ... are given. [ABSTRACT FROM AUTHOR]

This paper deals with a new two-dimensional Wigner-Ville nonlinear transforms and their basic properties. All known results of the one-dimensional Wigner-Ville transform are derived as special cases of the present work. [ABSTRACT FROM AUTHOR]

In this paper a relation between Bessel and Fourier Cosine transforms is obtained with the aid of Riemann-Liouville fractional integral. An application of this relation to weighted norm inequalities is given. [ABSTRACT FROM AUTHOR]

In this paper, we establish several very basic formulas relating convolution products, integral transforms and inverse integral transforms for functionals in L2(C0[0, T]). The expansion of functionals in L2(C0[0, T]) in terms of Fourier-Hermite functionals plays a key role. [ABSTRACT FROM AUTHOR]

In this paper, several properties associated with the complete monotonicity, the strongly complete monotonicity and the logarithmically complete monotonicity of functions related to the gamma and psi functions are obtained. Relevant connections of the results presented here with those derived in earlier works are also pointed out. [ABSTRACT FROM AUTHOR]

In this paper, we construct a system of bi-orthogonal trigonometric functions and we connect this system to a family of orthogonal functions on the unit circle that can be considered like generalized polynomials in the variable z1/2. Some properties such as recurrence relations, kernel representations and a Favard-type theorem are studied. [ABSTRACT FROM AUTHOR]

Generalized Cauchy transformation, actually the generalized Cauchy formula for functions, distributions and ultradistributions with appropriate growth rate, is given and used for the boundary value representation in the sense of generalized functions. [ABSTRACT FROM AUTHOR]

The Stockwell transform of a signal, i.e., a function in L2(), is defined as a hybrid of the Gabor transform and the wavelet transform. The continuous and discrete reconstruction formulas for a signal from its Stockwell transform are established. [ABSTRACT FROM AUTHOR]

We discuss the properties of the Hankel transformation of a sequence whose elements are the sums of consecutive generalized Catalan numbers and find their values in the closed form. [ABSTRACT FROM AUTHOR]