A Note on Convolution and Composite Convolution Operators

Shallu Sharma

doi:https://doi.org/10.14445/22315373/IJMTT-V36P529

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 36 | Number 3 | Year 2016 | Article Id. IJMTT-V36P529 | DOI : https://doi.org/10.14445/22315373/IJMTT-V36P529

A Note on Convolution and Composite Convolution Operators

Shallu Sharma

Citation :

Shallu Sharma, "A Note on Convolution and Composite Convolution Operators," International Journal of Mathematics Trends and Technology (IJMTT), vol. 36, no. 3, pp. 212-217, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V36P529

Abstract

In this note we obtain the condition for convolution and composite convolution operators to be bounded and Hermition .We also find that only the compact composite convolution operator is the Zero operator.

Keywords

Convolution product, Hermition operator, Bounded and Compact operator.

References

[1] Kaninska A and Musieelak J : “On convolution operator in Orlicz spaces" Revirta Mathematica de la, Universidad computense de Madrid, Vol 2, 151-158(1989)
[2] Komal, B. S and Gupta, D.K “ Normal composition operators.” Acta Sci. Math (Szeged) 47 (1984) 445-448.
[3] Komal, B.S and Sharma T.K, “ Composition operators on lp , 0 < p < 1”, Jammu University reviews Vol 1994, 41-48.
[4] Kumar. ”Composition operators on L2”, Thesis University of Jammu 1978.
[5] Komal B.S, Gupta, Anupama “On Composition Convolution operators with weight ” Int. Journal of Involution and Scientific research ISSN 2315-8014 Vol 23 No. 2 May 2016 PP 303-309.
[6] Nortgren, E.A “Composition operators on Hilbers spaces”, Lecture notes ion maths 693 Springer Velag, New York 37-63.
[7] Ridge, W.C “Composition operators”, Thesis Indiana University 1969.
[8] Singh R.K, Gupta DK and Komal B.S “Some results on Composition Operators on l2”, Int. J. Math and math. Soc. 2(1979), 29-34.
[9] Stepanov, V.D:“On convolution Integral operators", Soviet Math Dokal, 19, No. 6, 1978.
[10] Stepanov. V.D.“On boundedness and compactness of a class of convolution" soviet Math.Dokal 41, 446-470(1990).
[11] Singh R.K and Komal B.S.“Composition operators on p and its adjoint," Proc. Amer.Math.Soc. 70(1978), 21-25.