S. K. Upadhyay

On continuous Bessel wavelet transformation associated with the Hankel–Hausdorff operator

The main objective of this paper is to study the continuous Bessel wavelet transformation and its inversion formula, and the Parseval relation using the theory of the Hankel convolution. A relation between the Bessel wavelet transformation and the Hankel–Hausdorff operator is established.

Integrability of the continuum Bessel wavelet kernel

In this paper, the sufficient condition for the integrability of the kernel of the inverse Bessel wavelet transform is obtained by using the theory of Hankel transform and Hankel convolution.

Infinite pseudo-differential operators on WM(Rn) space

Abstract The infinite pseudo-differential operator on WM(Rn) space is introduced and its various properties are studied. A general class of symbols θ(x,ξ) is introduced and then it is proved that the pseudo-differential operator Aθφ is a continuous linear mapping from WM(Rn) into itself. An Lp(Rn)-boundedness result for the pseudo-differential operator associated with a general class of symbols σ(x,ξ) for ξ = u+it is obtained. It is shown that the pseudo-differential operator is a bounded linear operator from Lp(Rn) into Lp(Rn) for 1 < p < ∞. The Sobolev space of type Gs,p(Rn) is introduced and its properties are studied.

W-Spaces and Pseudo-differential Operators

In this article we improve the characterisation of [R.S. Pathak and S.K. Upadhyay (1994). W p -space and Fourier transformation. Proc. Amer. Math Soc ., 121 (3), 733-738.] and study the properties of pseudo-differential operator on the space , where z 1 , M 1 are convex functions and a, b are positive constants.

The relation between Bessel wavelet convolution product and Hankel convolution product involving Hankel transform

In this paper, the relation between Bessel wavelet convolution product and Hankel convolution product is obtained by using the Bessel wavelet transform and the Hankel transform. Approximation results of the Bessel wavelet convolution product are investigated by exploiting the Hankel transformation tool. Motivated from the results of Pinsky7, heuristic treatment of the Bessel wavelet transform is introduced and other properties of the Bessel wavelet transform are studied.

Continuous Watson wavelet transform

We generalize the results of [2], and using the theory of Watson convolution, the continuous Watson wavelet transform is defined. Some properties related to the Watson wavelet transform are studied.

Properties of the Hankel–Hausdorff operator on Hardy spaceH1(0,∞)

Abstract The main objective of this paper is to introduce the Hankel–Hausdorff operator of a function f ∈ L1(0,∞) generated on the Hardy space and to study its various properties in L1(0,∞).

Up μ-Spaces And hankel Transform

This paper extends the Hankel transformation to classes of generalized functions that behave like Lp spaces. Their constructions are reminiscent of Orlicz spaces. The paces are designed specifically for the Hankel transformation, and the associated derivations and manipulations are given. Hankel transform of generalized functions is defined and an operational-transform formula is obtained.

A Mathematical Model of Consumers' Buying Behaviour Based On Multiresolution Analysis.

Abstract In this paper we have presented a generalized mathematical model of consumers’ buying behaviour. This model provides better insights and perceptions that can be used to take many important managerial decisions for any product to improve the buying behaviour of consumers towards that product. In this paper we have proved that consumers’ buying behaviour is a L2(ℝ) function. Such functions can take two values. 1 (if the buying behaviour is satisfied) or 0 (if the buying behaviour is not satisfied). Through multiresolution analysis (MRA), we have proved that all the factors affecting consumers’ buying behaviour are the subspaces of L2(ℝ). We have also proved that the satisfaction of consumers’ buying behaviour is convex with respect to all the factors that affect it. We have given a relationship among all the factors influencing consumers’ buying behaviour.We have provided a way by which the overall inclination of buying behaviour of any consumer or his inclination towards any particular product can be investigated.

Wavelet convolution product involving fractional fourier transform

Abstract Exploiting the theory of fractional Fourier transform, the wavelet convolution product and existence theorems associated with the n-dimensional wavelet transform are investigated and their properties studied.