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On the Green function of the killed fractional Laplacian on the periodic domain

  • Thomas Simon
Veröffentlicht/Copyright: 28. Oktober 2021
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Fractional Calculus and Applied Analysis
Aus der Zeitschrift Fractional Calculus and Applied Analysis Band 24 Heft 5

Abstract

We give a very simple proof of the positivity and unimodality of the Green function for the killed fractional Laplacian on the periodic domain. The argument relies on the Jacobi triple product and a probabilistic representation of the Green function. We also show by a contour integration that the Green function is completely monotone on the positive part of the periodic domain.

MSC 2010: Primary 34A08; Secondary 60G52
Key Words: completely monotone function; fractional Laplacian; Green function; Jacobi triple product

References

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[3] R. L. Frank and E. Lenzmann, Uniqueness of non-linear ground states for fractional Laplacian in R. Acta Math. 210 (2013), 261–318; DOI: 10.1007/s11511-013-0095-9.10.1007/s11511-013-0095-9Suche in Google Scholar

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[5] U. Le and D. E. Pelinovsky, Green’s function for the fractional KdV equation on the periodic domain via Mittag-Leffler’s function. Fract. Calc. Appl. Anal. 24, No 5 (2021), 1507–1534; DOI:10.1515/fca-2021-0063https://www.degruyter.com/journal/key/fca/24/5/htmlSuche in Google Scholar

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Received: 2021-01-24
Revised: 2021-09-15
Published Online: 2021-10-28
Published in Print: 2021-10-26

© 2021 Diogenes Co., Sofia

Artikel in diesem Heft

  1. Frontmatter
  2. Editorial
  3. FCAA related news, events and books
  4. Survey Paper
  5. Towards a unified theory of fractional and nonlocal vector calculus
  6. Research Paper
  7. An adaptive memory method for accurate and efficient computation of the Caputo fractional derivative
  8. Analysis of solutions of some multi-term fractional Bessel equations
  9. Existence of solutions for the semilinear abstract Cauchy problem of fractional order
  10. Summability of formal solutions for a family of generalized moment integro-differential equations
  11. Analysis and fast approximation of a steady-state spatially-dependent distributed-order space-fractional diffusion equation
  12. Green’s function for the fractional KdV equation on the periodic domain via Mittag–Leffler function
  13. First order plus fractional diffusive delay modeling: Interconnected discrete systems
  14. On a solution of a fractional hyper-Bessel differential equation by means of a multi-index special function
  15. On the decomposition of solutions: From fractional diffusion to fractional Laplacian
  16. Output error MISO system identification using fractional models
  17. Short Paper
  18. Identification of system with distributed-order derivatives
  19. Short note
  20. On the Green function of the killed fractional Laplacian on the periodic domain
https://doi.org/10.1515/fca-2021-0069
Schlagwörter für diesen Artikel
completely monotone function; fractional Laplacian; Green function; Jacobi triple product

Artikel in diesem Heft

  1. Frontmatter
  2. Editorial
  3. FCAA related news, events and books
  4. Survey Paper
  5. Towards a unified theory of fractional and nonlocal vector calculus
  6. Research Paper
  7. An adaptive memory method for accurate and efficient computation of the Caputo fractional derivative
  8. Analysis of solutions of some multi-term fractional Bessel equations
  9. Existence of solutions for the semilinear abstract Cauchy problem of fractional order
  10. Summability of formal solutions for a family of generalized moment integro-differential equations
  11. Analysis and fast approximation of a steady-state spatially-dependent distributed-order space-fractional diffusion equation
  12. Green’s function for the fractional KdV equation on the periodic domain via Mittag–Leffler function
  13. First order plus fractional diffusive delay modeling: Interconnected discrete systems
  14. On a solution of a fractional hyper-Bessel differential equation by means of a multi-index special function
  15. On the decomposition of solutions: From fractional diffusion to fractional Laplacian
  16. Output error MISO system identification using fractional models
  17. Short Paper
  18. Identification of system with distributed-order derivatives
  19. Short note
  20. On the Green function of the killed fractional Laplacian on the periodic domain
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