Examples



mdbootstrap.com



 
Статья
2018

A Criterion of Convergence of Lagrange–Sturm–Liouville Processes in Terms of One-Sided Module of Variation


A. Yu. TryninA. Yu. Trynin
Русская математика
https://doi.org/10.3103/S1066369X1808008X
Abstract / Full Text

We obtain a criterion of uniform convergence inside the interval (0, π) of interpolation processes determined by eigenfunctions of the regular Sturm–Liouville problem with a continuous potential of bounded variation. The criterion is formulated in terms of one-sided modulus of variation.

Author information
  • Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012, RussiaA. Yu. Trynin
References
  1. Natanson, G. I. “On Certain Interpolation Process”, Uchen. zap. Leningrad Ped. Inst. 166, 213–219 (1958) [Russian].
  2. Trynin, A. Yu. “The Divergence of Lagrange Interpolation Processes in Eigenfunctions of the Sturm–Liouville Problem”, RussianMathematics 54, No. 11, 66–76 (2010).
  3. Trynin, A. Yu. “Absence of Stability of InterpolationWith Respect to Eigenfunctions of the Sturm–Liouville Problem”, RussianMathematics 44, No. 9, 58–71 (2000).
  4. Trynin, A. Yu. “Differential Properties of Zeros of Eigenfunctions of the Sturm-Liouville Problem”, Ufim. Mat. Zh. 3, No. 4, 133–143 (2011) [Russian].
  5. Trynin, A. Yu. “On Inverse Nodal Problem for Sturm–Liouville Operator”, UfaMath. J. 5, No. 4, 112–124 (2013).
  6. Novikov, I. Ya., Stechkin, S. B. “Foundations ofWavelet Theory”, Russ. Math. Surv. 53, No. 6, 1159–1231 (1998).
  7. Livne Oren, E., Brandt Achi, E. “TheMultilevel Sync Transform”, SIAM J. on Sci. Comp. 33, No. 4, 1726–1738 (2011).
  8. Coroianu, L., Sorin, G. “Localization Results for the Non-Truncated max-Product Sampling Operators Based on Fejer and Sinc-Type Kernels”, DemonstratioMath. 49, No. 1, 38–49 (2016).
  9. Richardson, M., Trefethen, L. “A Sinc Function Analogue of Chebfun”, SIAM J. Sci. Comput. 33, No. 5 2519–2535 (2011).
  10. Khosrow, M., Yaser, R., Hamed, S. “Numerical Solution for FirstKind Fredholm Integral Equations by Using Sinc CollocationMethod”, International J. Appl. Phys. and Math. 6, No. 3, 120–128 (2016).
  11. Marwa, M. “Sinc Approximation of Eigenvalues of Sturm–Liouville Problems With a Gaussian Multiplier”, Calcolo: a quarterly on numerical analysis and theory of computation 51, No. 3, 465–484 (2014).
  12. Trynin, A. Yu., Sklyarov, V. P. “Error of Sinc Approximation of Analytic Functions on an Interval”, Sampling Theory in Signal and Image Processing, 7, No. 3, 263–270 (2008).
  13. Trynin, A. Yu. “Tests for Pointwise and Uniform Convergence of Sinc Approximations of Continuous Functions on a Closed Interval”, Sb.Math. 198, No. 10, 1517–1534.
  14. Umakhanov, A. Ya., Sharaputdinov, I.‘I. “Interpolation of Functions by Whittaker’s Sums and TheirModifications: Criteria for Uniform Convergence”, Vladikavkazsk.Mat. Zh. 18, No. 4, 61–70 (2016) [Russian].
  15. Trynin, A. Yu. “A Generalization of the Whittaker–Kotel’nikov–Shannon Sampling Theorem for Continuous Functions on a Closed Interval”, Sb.Math. 200, No. 11, 1633–1679 (2009).
  16. D’yachenko M.I. “On a Class of Summability Methods for Multiple Fourier Series”, Sb.Math. 204, No. 3, 307–322 (2013).
  17. Skopina, M. A., Maksimenko, I. E. “Many-Dimensional Periodic Wavelets”, Algebra i Analiz 15, No. 2, 1–39 (2003) [Russian].
  18. Farkov, Yu. A. “On the Best Linear Approximation of Holomorphic Functions”, Fundament. i Prikl. Matem. 19, No. 5, 185–212 (2014) [Russian].
  19. Sansone J. Ordinary Differential Equations (In. Lit.,Moscow, 1953) [Russian translation].
  20. Levitan B.M., Sargsyan I.S. Sturm–Liouville and Dirac Operators [Russian] (Nauka, Moscow, 1988).
  21. Privalov A.A. Theory of Interpolation of Functions (Saratov Univ. Press, 1990), Vol. 1 [Russian].
  22. Privalov A.A. Theory of Interpolation of Functions (Saratov Univ. Press, 1990), Vol. 2 [Russian].