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Some Results on Shannon Wavelets and Wavelets Frames

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Abstract

In this article, Shannon wavelets are studied together with their properties and we focused on Shannon wavelets and scalar functions through linear algebraic concept such as linearly independent, nested properties and direct product etc. Also, we generated Laguerre wavelets frames and discussed some results on it.

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References

  1. Cattani, C.: Harmonic wavelets towards the solution of nonlinear PDE. Comput. Math. Appl. 50, 1191–1210 (2005)

    Article  MathSciNet  Google Scholar 

  2. Shiralashetti, S.C., Kumbinarasaiah, S.: Some results on Haar wavelets matrix through linear algebra. Wavelets Linear Algebra 4(2), 49–59 (2017)

    Google Scholar 

  3. Shiralashetti, S.C., Kumbinarasaiah, S.: Cardinal B-spline wavelet based numerical method for the solution of generalized Burgers–Huxley equation. Int. J. Appl. Comput. Math. 4, 73 (2018). https://doi.org/10.1007/s40819-018-0505-y

    Article  MathSciNet  MATH  Google Scholar 

  4. Shiralashetti, S.C., Kumbinarasaiah, S.: Theoretical study on continuous polynomial wavelet bases through wavelet series collocation method for nonlinear Lane–Emden type equations. Appl. Math. Comput. 315, 591–602 (2017)

    MathSciNet  Google Scholar 

  5. Shiralashetti, S.C., Kumbinarasaiah, S.: Hermite wavelets operational matrix of integration for the numerical solution of nonlinear singular initial value problems. Alex. Eng. J. (2017). https://doi.org/10.1016/j.aej.2017.07.014

  6. Cattani, C.: Shannon wavelets for the solution of integrodifferential equations. Math. Probl. Eng. 2010, 1–22 (2010)

    MathSciNet  MATH  Google Scholar 

  7. Cattani, C.: Shannon wavelet analysis. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) Computational Science ICCS 2007. Lecture Notes in Computer Science, vol. 4488. Springer, Berlin (2007)

    Google Scholar 

  8. Cattani, C.: Harmonic wavelet solutions of the Schrodinger equation. Int. J. Fluid Mech. Res. 5, 1–10 (2003)

    MathSciNet  Google Scholar 

  9. Cattani, C., Kudreyko, A.: Application of periodized harmonic wavelets towards solution of eigenvalue problems for integral equations. Math. Probl. Eng. 2010, 1–8 (2010)

    MATH  Google Scholar 

  10. Cattani, C.: Fractional calculus and Shannon wavelet. Math. Probl. Eng. 2012, 1–26 (2012)

    MathSciNet  MATH  Google Scholar 

  11. Shi, Z., Li, F.: Numerical solution of high-order differential equations by using periodized Shannon wavelets. Appl. Math. Model. 38, 2235–2248 (2014)

    Article  MathSciNet  Google Scholar 

  12. Cattani, C.: Shannon wavelets theory. Math. Probl. Eng. 2008, 1–24 (2008)

    MathSciNet  MATH  Google Scholar 

  13. Kovacevic, J., Chebira, A.: Life beyond bases: the advent of frames (part I). IEEE Signal Process. Mag. 86, 1–19 (2007)

    Google Scholar 

  14. Kovacevic, J., Chebira, A.: Life beyond bases: the advent of frames (part II). IEEE Signal Process. Mag. 115, 1–11 (2007)

    Google Scholar 

  15. Heil, C.: A Basis Theory Primer. Applied and Numerical Harmonic Analysis. Springer, New York (1998)

    Google Scholar 

  16. Rajaraman, R., Hariharan, G.: An efficient wavelet based spectral method to singular boundary value problems. J. Math. Chem. 53, 2095–2113 (2015)

    Article  MathSciNet  Google Scholar 

  17. Duggan, R., Goodman, A.: Pointwise bounds for a nonlinear heat conduction model of the human head. Bull. Math. Biol. 48(2), 229–236 (1986)

    Article  Google Scholar 

  18. Zhou, F., Xu, X.: Numerical solution for the linear and nonlinear singular boundary value problems using Lagurre wavelets. Adv. Differ. Equ. (2016). https://doi.org/10.1186/s13662-016-0754-1

Download references

Acknowledgements

Acknowledge the support received from the University Grants Commission (UGC), Govt. of India for Grant under UGC-SAP DRS-III for 2016-2021:F.510/3/DRS-III/2016(SAP-I) Dated: 29th Feb. 2016.

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  1. Department of Mathematics, Karnatak University in Dharwad, Dharwad, India

    S. C. Shiralashetti & S. Kumbinarasaiah

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  1. S. C. Shiralashetti
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  2. S. Kumbinarasaiah
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Correspondence to S. C. Shiralashetti.

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Shiralashetti, S.C., Kumbinarasaiah, S. Some Results on Shannon Wavelets and Wavelets Frames. Int. J. Appl. Comput. Math 5, 10 (2019). https://doi.org/10.1007/s40819-018-0596-5

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  • DOI: https://doi.org/10.1007/s40819-018-0596-5

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