Paley–Wiener–Schwartz type theorem for the wavelet transform

ABSTRACT

In the present paper, we discuss about extension of the wavelet transform on distribution space of compact support and develop the Paley–Wiener–Schwartz type theorem for the wavelet transform on the same. Furthermore, Paley–Wiener–Schwartz type theorem for the wavelet transform is also established using the relation between the wavelet transform and double Fourier transform.

KEYWORDS:

• Distribution space
• infraexponential decaying wavelets
• Fourier transform
• double Fourier transform
• wavelet transform

AMS SUBJECT CLASSIFICATIONS:

• Primary: 44A15
• 42C15
• Secondary: 46F12

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The second author was supported in part by the University Grants Commission [Sanction No. F. 4-2/2006(BSR)/13-663/2012].