Construction of frame relative to $n$-Hilbert space

Subject Areas : Functional analysis

P. Ghosh ¹ (Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata, 700019, West Bengal, India)
T. K. Samanta ² (Department of Mathematics, Uluberia College, Uluberia, Howrah, 711315, West Bengal, India)

Received: 2020-08-07 Accepted : 2021-06-15 Published : 2021-06-01

Keywords:

References:

[1] A. A. Arefijamaal, G. Sadeghi, Frames in 2-inner product spaces, Iran. J. Math. Sci. Inform. 8 (2) (2013), 123-130.

[2] Y. J. Cho, S. S. Kim, A. Misiak, Theory of 2-Inner Product Spaces, Nova Science Publishes, New York, 2001.

[3] O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser, 2008.

[4] R. J. Duffin, A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952), 341-366.

[5] I. Daubechies, A. Grossmann, Y. Mayer, Painless nonorthogonal expansions, J. Math. Physics. 27 (5) (1986), 1271-1283.

[6] C. Diminnie, S. Gahler, A. White, 2-inner product spaces, Demonstratio Math. 6 (1973), 525-536.

[7] D. Gabor, Theory of communications, J. Inst. Elec. Engrg. 93 (1946), 429-457.

[8] H. Gunawan, On n-inner products, n-norm, and the Cauchy-Schwarz inequality, Sci. Math. Jpn. 55 (2002), 53-60.

[9] H. Gunawan, M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci. 27 (2001), 631-639.

[10] H. Heuser, Functional Analysis, Wiley, New York, 1982.

[11] E. Kreyzig, Introductory Functional Analysis with Applications, Wiley, New York, 1989.

[12] A. Misiak, n-inner product spaces, Math. Nachr. 140 (1989), 299-319.