Affiliation:
1. Department of Mathematics, Faculty of Sciences, Ondokuz Mayıs University, Samsun, Turkey.
Abstract
In this study, we describe a linear space A_(α,p(.))^(w,ν) (R^d ) of functions f∈L_w^1 (R^d ) whose fractional Fourier transforms F_α f belong to L_ν^p(.) (R^d ) for p^+<∞. We show that A_(α,p(.))^(w,ν) (R^d ) becomes a Banach algebra with the sum norm ‖f‖_(A_(α,p(.))^(w,ν) )=‖f‖_(1,w)+‖F_α f‖_(p(.),ν) and under Θ (fractional convolution) convolution operation. Besides, we indicate that the space A_(α,p(.))^(w,ν) (R^d ) is an abstract Segal algebra, where w is weight function of regular growth. Moreover, we find an approximate identity for A_(α,p(.))^(w,ν) (R^d ). We also discuss some other properties of A_(α,p(.))^(w,ν) (R^d ). Finally, we investigate some inclusions of this space.
Publisher
Valahia University of Targoviste - Journal of Science and Arts
Reference28 articles.
1. Rudin, W., Functional Analysis, Mc Graw-Hill, New York, 1973.
2. Rudin, W., Real and Complex Analysis, McGraw-Hill, New York, 1966.
3. Gröchenig, K., Weight functions in time-frequency analysis, in: Pseudodifferential Operators: Partial Differential Equations and Time-Frequency Analysis, Fields Inst. Commun. 52, 343-366, Amer. Math. Soc., Providence, RI, 2007.
4. Reiter, H., Stegeman, J. D., Classical Harmonic Analysis and Locally Compact Group, Clarendon Press, Oxford, 2000.
5. Feichtinger, H. G., Gürkanlı, A, T., Internat. J. Math. Sci., 13, 517, 1990.