DOI QR코드

DOI QR Code

SLANT H-TOEPLITZ OPERATORS ON THE HARDY SPACE

  • Gupta, Anuradha (Department of Mathematics Delhi college of Arts and Commerce University of Delhi) ;
  • Singh, Shivam Kumar (Department of Mathematics University of Delhi)
  • Received : 2018.05.10
  • Accepted : 2018.08.13
  • Published : 2019.05.01

Abstract

The notion of slant H-Toeplitz operator $V_{\phi}$ on the Hardy space $H^2$ is introduced and its characterizations are obtained. It has been shown that an operator on the space $H^2$ is a slant H-Toeplitz if and only if its matrix is a slant H-Toeplitz matrix. In addition, the conditions under which slant Toeplitz and slant Hankel operators become slant H-Toeplitz operators are also obtained.

Acknowledgement

Supported by : CSIR Research

References

  1. S. C. Arora and S. Paliwal, On H-Toeplitz operators, Bull. Pure Appl. Math. 1 (2007), no. 2, 141-154.
  2. J. H. Clifford and D. Zheng, Composition operators on the Hardy space, Indiana Univ. Math. J. 48 (1999), no. 4, 1585-1616.
  3. C. C. Cowen, Composition operators on $H^2$, J. Operator Theory 9 (1983), no. 1, 77-106.
  4. G. Datt and R. Aggarwal, A generalization of slant Toeplitz operators, Jordan J. Math. Stat. 9 (2016), no. 2, 73-92.
  5. G. Datt and R. Aggarwal, A note on the operator equation generalizing the notion of slant Hankel operators, Anal. Theory Appl. 32 (2016), no. 4, 387-395. https://doi.org/10.4208/ata.2016.v32.n4.6
  6. T. N. T. Goodman, C. A. Micchelli, and J. D. Ward, Spectral radius formulas for subdivision operators, in Recent advances in wavelet analysis, 335-360, Wavelet Anal. Appl., 3, Academic Press, Boston, MA.
  7. C. Heil, G. Strang, and V. Strela, Approximation by translates of refinable functions, Numer. Math. 73 (1996), no. 1, 75-94. https://doi.org/10.1007/s002110050185
  8. M. C. Ho, Properties of slant Toeplitz operators, Indiana Univ. Math. J. 45 (1996), no. 3, 843-862.
  9. M. C. Ho, Spectra of slant Toeplitz operators with continuous symbols, Michigan Math. J. 44 (1997), no. 1, 157-166. https://doi.org/10.1307/mmj/1029005627
  10. G. Strang and V. Strela, Orthogonal multiwavelets with vanishing moments, Optical Engineering 33 (1994), no. 7, 2104-2107. https://doi.org/10.1117/12.172247
  11. G. Strang and V. Strela, Short wavelets and matrix dilation equations, IEEE Trans. Signal Process. 43 (1995), no. 1, 108-115. https://doi.org/10.1109/78.365291
  12. L. F. Villemoes, Wavelet analysis of refinement equations, SIAM J. Math. Anal. 25 (1994), no. 5, 1433-1460. https://doi.org/10.1137/S0036141092228179
  13. T. Zegeye and S. C. Arora, The compression of slant Toeplitz operator to $H^2({\partial}D)$, Indian J. Pure Appl. Math. 32 (2001), no. 2, 221-226.
  14. T. Zegeye and S. C. Arora, The compression of a slant Hankel operator to $H^2$, Publ. Inst. Math. (Beograd) (N.S.) 74(88) (2003), 129-136. https://doi.org/10.2298/PIM0374129Z