Sławomir Michalik. List of publications and manuscripts

List of publications

  1. On sequences preserving q-Gevrey asymptotic expansions, Anal. Math. Phys. 14, 17 (2024) (together with Alberto Lastra); (arXiv:2304.09294).
  2. On the summability and convergence of formal solutions of linear q-difference-differential equations with constant coefficients, Math. Ann. (2023), https://doi.org/10.1007/s00208-023-02672-0 (together with Kunio Ichinobe); (enhanced pdf, arXiv:2301.10331).
  3. On polyharmonic polynomials, Acta Math. Hungar. 169, 325-348 (2023) (together with Hubert Grzebuła); (arXiv:2204.05430).
  4. Some notes on moment partial differential equations. Application to fractional functional equations, in Recent Trends in Formal and Analytic Solutions of Diff. Equations, Contemporary Mathematics, vol. 782, Amer. Math. Soc., Providence, RI, 2023, 219-228 (together with Alberto Lastra and Maria Suwińska).
  5. Multisummability of formal solutions for a family of generalized singularly perturbed moment differential equations, Results Math 78:49 (2023) (together with Alberto Lastra and Maria Suwińska); (arXiv:2202.05377).
  6. Summable solutions of the Goursat problem for some partial differential equations with constant coefficients, J. Differential Equations 304 (2021), 435-466; (arXiv:2103.15879).
  7. Summability of formal solutions for a family of generalized moment integro-differential equations, Fract. Calc. Appl. Anal. 24 (2021), 1445–1476 (together with Alberto Lastra and Maria Suwińska); (arXiv:2012.12323).
  8. Estimates of formal solutions for some generalized moment partial differential equations, J. Math. Anal. Appl. 500:125094 (2021) (together with Alberto Lastra and Maria Suwińska); (arXiv:1911.11998).
  9. Summability of formal solutions for some generalized moment partial differential equations, Results Math. 76:22 (2021) (together with Alberto Lastra and Maria Suwińska); (arXiv:2007.08764).
  10. Gevrey estimates for certain moment partial differential equations, Complex Differential and Difference Equations, De Gruyter Proceedings in Mathematics (2020), 391-408 (together with Maria Suwińska); (arXiv:1812.10698).
  11. The Stokes phenomenon for some moment partial differential equations, J. Dyn. Control Syst. 25 (2019), 573-598 (together with Bożena Tkacz); (Enhanced PDF, arXiv:1806.03520).
  12. Spherical polyharmonics and Poisson kernels for polyharmonic functions, Complex Var. Elliptic Equ. 64 (2019), 420-442, (together with Hubert Grzebuła); (arXiv:1706.01297).
  13. Hyperasymptotic solutions for certain partial differential equations, Formal and Analytic Solutions of Diff. Equations, Springer Proceedings in Mathematics & Statistics 256 (2018), 61-78 (together with Maria Suwińska); (arXiv:1804.09734).
  14. Analytic and summable solutions of inhomogeneous moment partial differential equations, Funkcial. Ekvac. 60 (2017), 325-351; (arXiv:1505.06724).
  15. A Dirichlet type problem for complex polyharmonic functions, Acta Math. Hungar. 153 (2017), 216-229 (together with Hubert Grzebuła); (arXiv:1610.04928).
  16. The Stokes phenomenon for certain partial differential equations with meromorphic initial data, Asymptot. Anal. 99 (2016), 163-182 (together with Bożena Podhajecka); (arXiv:1603.04209).
  17. Summable solutions of some partial differential equations and generalised integral means, J. Math. Anal. Appl. 444 (2016), 1242-1259; (arXiv:1502.02462).
  18. Summability of formal solutions of linear partial differential equations with divergent initial data, J. Math. Anal. Appl. 406 (2013), 243-260; (arXiv:1303.1555).
  19. Analytic solutions of moment partial differential equations with constant coefficients , Funkcial. Ekvac. 56 (2013), 19-50.
  20. On Borel summable solutions of the multidimensional heat equation, Ann. Polon. Math. 105 (2012), 167-177.
  21. Multisummability of formal solutions of inhomogeneous linear partial differential equations with constant coefficients, J. Dyn. Control Syst. 18 (2012), 103-133.
  22. On the multisummability of divergent solutions of linear partial differential equations with constant coefficients, J. Differential Equations 249 (2010), 551-570 (with: Corrigendum to "On the multisummability of divergent solutions of linear partial differential equations with constant coefficients" [J. Differential Equations 249 (2010), 551-570], J. Differential Equations 255 (2013), 2400-2401).
  23. Summability and fractional linear partial differential equations, J. Dyn. Control Syst. 16 (2010), 557-584.
  24. Laplace ultradistributions supported by a cone, Banach Center Publ. 88 (2010), 229-241.
  25. Summability of formal solutions to the n-dimensional inhomogeneous heat equation, J. Math. Anal. Appl. 347 (2008), 323-332.
  26. Formal solutions of semilinear heat equations, J. Math. Anal. Appl. 341 (2008), 372-385 (together with Grzegorz Łysik).
  27. Summability of divergent solutions of the n-dimensional heat equation, J. Differential Equations 229 (2006), 353-366.
  28. The Cauchy kernel for cones, Studia Math. 163 (2004), 21-39.
  29. Laplace distributions and hyperfunctions on simplicial cones, Integral Transforms Spec. Funct. 14 (2003), 307-320.
  30. The kernel theorem for Laplace ultradistributions, Ann. Polon. Math. 77 (2001), 209-217.

List of manuscripts and papers in preparation

  1. On the characterization of formal automorphisms of integro-differential operators, submitted (together with Alberto Lastra and Maria Suwińska); (arXiv:2306.06398).
  2. On the summability of formal solutions to some linear partial differential equations, manuscript (mp_arc).
  3. On the characterization of automorphisms of integro-differential operators in Gevrey classes, in preparation (together with Alberto Lastra and Maria Suwińska).
  4. On the q-summability of formal solutions of linear q-difference-differential equations with constant coefficients, in preparation (together with Alberto Lastra and Kunio Ichinobe).

Last modification: February 25, 2024

Sławomir Michalik