[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c160204

APPLICATIONS ON THE BESSEL-STRUVE-TYPE FOCK SPACE

Soltani, Fethi (Department of Mathematics Faculty of Science Jazan University)

Publication Information

Communications of the Korean Mathematical Society / v.32, no.4, 2017 , pp. 875-883 More about this Journal

Abstract

In this work, we establish Heisenberg-type uncertainty principle for the Bessel-Struve Fock space ${\mathbb{F}}_{\nu}$ associated to the Airy operator $L_{\nu}$ . Next, we give an application of the theory of extremal function and reproducing kernel of Hilbert space, to establish the extremal function associated to a bounded linear operator $T:{\mathbb{F}}_{\nu}{\rightarrow}H$ , where H be a Hilbert space. Furthermore, we come up with some results regarding the extremal functions, when T are difference operators.

Keywords

Bessel-Struve-type Fock space; Heisenberg-type uncertainty principle; extremal functions;

Citations & Related Records

Reference

1	F. Soltani, Operators and Tikhonov regularization on the Fock space, Integral Transforms Spec. Funct. 25 (2014), no. 4, 283-294. DOI
2	F. Soltani, Some examples of extremal functions on the Fock space F(C), Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb. 42 (2016), no. 2, 265-272.
3	G. N. Watson, A Treatise on Theory of Bessel Functions, Cambridge, MA: Cambridge University Press, 1966.
4	S. Saitoh, Approximate real inversion formulas of the Gaussian convolution, Appl. Anal. 83 (2004), no. 7, 727-733. DOI
5	A. Abouelaz, A. Achak, R. Daher, and N. Safouane, Harmonic analysis associated with the generalized Bessel-Struve operator on the real line, Int. Refereed J. Eng. Sci. 4 (2015), 72-84.
6	V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform, Comm. Pure Appl. Math. 14 (1961), 187-214. DOI
7	C. A. Berger and L. A. Coburn, Toeplitz operators and quantum mechanics, J. Funct. Anal. 68 (1986), no. 3, 273-299. DOI
8	G. Folland, Harmonic analysis on phase space, Annals of Mathematics Studies 122, Princeton University Press, Princeton, New Jersey, 1989.
9	F. M. Cholewinski, Generalized Fock spaces and associated operators, SIAM. J. Math. Anal. 15 (1984), no. 1, 177-202. DOI
10	A. Erdely et al., Higher Transcendental Functions. vol 2, McGraw-Hill, New-York, 1953.
11	A. Gasmi and M. Si, The Bessel-Struve intertwining operator on C and mean-periodic functions, Int. J. Math. Math. Sci. 2004 (2004), no. 57-60, 3171-3185. DOI
12	A. Gasmi and F. Soltani, Fock spaces for the Bessel-Struve kernel, J. Anal. Appl. 3 (2005), no. 2, 91-106.
13	K. Grochenig, Foundations of time-frequency analysis, Birkhauser, Boston, 2001.
14	S. Hamem, L. Kamoun, and S. Negzaoui, Cowling-Price type theorem related to Bessel- Struve transform, Arab J. Math. Sci. 19 (2013), no. 2, 187-198. DOI
15	C. A. Berger and L. A. Coburn, Toeplitz operators on the Segal-Bargmann space, Trans. Amer. Math. Soc. 301 (1987), no. 2, 813-829. DOI
16	L. Kamoun and S. Negzaoui, An $L^p$ - $L^q$ -version of Morgan's theorem for Bessel-Struve transform, Asian-Eur. J. Math. 7 (2014), no. 1, 1450014, 7 pp. DOI
17	L. Kamoun and M. Si, Bessel-Struve intertwining operator and generalized Taylor series on the real line, Integral Transforms Spec. Funct. 16 (2005), no. 1, 39-55. DOI
18	S. Negzaoui, Beurling-Hormander's theorem related to Bessel-Struve transform, Integral Transforms Spec. Funct. 27 (2016), no. 9, 685-697. DOI
19	S. Saitoh, Hilbert spaces induced by Hilbert space valued functions, Proc. Amer. Math. Soc. 89 (1983), no. 1, 74-78. DOI
20	S. Saitoh, The Weierstrass transform and an isometry in the heat equation, Appl. Anal. 16 (1983), no. 1, 1-6. DOI
21	F. Soltani, Toeplitz and translation operators on the q-Fock spaces, Adv. Pure Math. 1 (2011), 325-333. DOI
22	S. Saitoh, Best approximation, Tikhonov regularization and reproducing kernels, Kodai Math. J. 28 (2005), no. 2, 359-367. DOI
23	F. Soltani, Generalized Fock spaces and Weyl commutation relations for the Dunkl kernel, Pacic J. Math. 214 (2004), no. 2, 379-397. DOI
24	F. Soltani, Multiplication and translation operators on the Fock spaces for the q-modied Bessel function, Adv. Pure Math. 1 (2011), 221-227. DOI
25	F. Soltani, Fock spaces for the q-Bessel-Struve kernel, Bull. Math. Anal. Appl. 4 (2012), no. 2, 1-16.