Vishvesh Kumar at Virtual Math Fest

Vishvesh PhotoVishvesh Kumar has just given a nice talk at the Virtual Math Fest 2020 (Symposium on Analysis and PDE)

The talk was about Lp-Lq boundedness of Fourier multipliers associated with the anharmonic oscillator,

on the joint work with Marianna Chatzakou from Imperial College London.

Well done, Vishvesh!

  • Chatzakou M., Kumar V., Lp-Lq boundedness of Fourier multipliers associated with the anharmonic oscillator. arxiv
  • Chatzakou M., Delgado J., Ruzhansky M., On a class of anharmonic oscillators. arxiv
  • Cardona D., Kumar V., Ruzhansky M., Tokmagambetov N., LpLq boundedness of pseudo-differential operators on smooth manifolds and its applications to nonlinear equationsarxiv

Watch the talk on YouTube

Vishvesh zoom

Linda Botchway starting her PhD

Congratulations to Linda Botchway, for receiving the grant of USD 15,500 from the Carnegie Corporation of New York (CCNY), for her PhD at the University of Ghana, Legon, under our supervision.

Linda Well done, Linda!

We are looking forward to Linda’s visits to our Analysis & PDE Center at Ghent University, and to her enrolment to UGent PhD program for a joint PhD.

 

Research of Linda on pseudo-differential operators on {\mathbb Z}^n started while she was a Master student at AIMS Ghana. This resulted in a substantial (41 pages) publication, a great achievement for a Master Student:

linda-gael

Botchway L., Kibiti G., Ruzhansky M., Difference equations and pseudo-differential operators on ZnJ. Funct. Anal.278 (2020), no. 11, 108473, 41pp. link (open access)arxiv

300px-SquareLattice.svgIn the above paper one makes a consistent development of the calculus of pseudo-differential operators which can be called pseudo-difference operators in the context of the lattice {\mathbb Z}^n Some interesting questions to answer:

    • how to define Hörmander type or other symbol classes on {\mathbb Z}^n?
    • what is the relation to the analysis on the torus {\mathbb T}^n?
    • can it be used to derive new properties of operators on {\mathbb Z}^n?
    • how to apply it to solving difference equations and to finding properties of their solutions?

WhatsApp Image 2020-03-08 at 9.02.42 PM

Dr Durvudkhan Suragan on Kazakh TV

file_000Another of our former postdocs (still at Imperial College London), and an associated collaborator of our Ghent Analysis and PDE Centre, Dr Durvudkhan Suragan, featured on Kazakh TV, in a special program about him and his achievements.

Congratulations, Durvudkhan!

It is very rewarding to see current and former students and postdocs being recognised for their achievements!

Watch it on Youtube:

TV Durvudkhan

Also, with the appearance of Dr Berikbol Torebek:

TV Berikbol

Recently: another of our associated member, Dr Erkinjon Karimov, on Uzbek State TV, read here.

Erkin on TV

Our books with Durvudkhan Suragan:

  1. Ashyralyev A., Kalmenov T., Ruzhansky M., Sadybekov M., Suragan D. (Eds.) Functional Analysis in Interdisciplinary Applications II, Springer Proceedings in Mathematics & Statistics, Springer, 2020, to appear
  2. Ruzhansky M., Suragan D., Hardy inequalities on homogeneous groups: 100 years of Hardy inequalities, Progress in Mathematics, Vol. 327, Birkhauser, 2019. xvi+588pp. link, free download (open access book), poster, the winner of  Ferran Sunyer I Balaguer Prize 2018
  3. Ruzhansky M., Sadybekov M., Suragan D., Spectral geometry of partial differential operators, Monographs and Research Notes in Mathematics, Chapman and Hall/CRC Press, 2020. 378pp. link, free download (open access book), poster

Our papers with Durvudkhan Suragan:

  1. Restrepo J., Ruzhansky M., Suragan D., Explicit representations of solutions for linear fractional differential equations with variable coefficients. arxiv
  2. Kassymov A., Ruzhansky M., Suragan D., Reverse Stein-Weiss, Hardy-Littlewood-Sobolev, Hardy, Sobolev and Caffarelli-Kohn-Nirenberg inequalities on homogeneous groups, arxiv
  3. Kassymov A., Ruzhansky M., Suragan D., Reverse integral Hardy inequalities on metric measure spaces. arxiv
  4. Ruzhansky M., Sabitbek B., Suragan D., Geometric Hardy inequalities on starshaped sets. arxiv
  5. Ruzhansky M., Sabitbek B., Suragan D., Geometric Hardy and Hardy-Sobolev inequalities on Heisenberg groups. Bull. Math. Sci., to appear. arxiv
  6. Kassymov A., Ruzhansky M., Suragan D., Anisotropic fractional Gagliardo-Nirenberg, weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type inequalities, and applications to Riesz potentials and p-sub-Laplacian systems. arxiv
  7. Ruzhansky M., Sabitbek B., Suragan D., Subelliptic geometric Hardy type inequalities on half-spaces and convex domainsAnn. Funct. Anal., to appear. arxiv
  8. Ruzhansky M., Suragan D., Yessirkegenov N., Euler semigroup, Hardy-Sobolev and Gagliardo-Nirenberg type inequalities on homogeneous groups. Semigroup Forum, to appear. link (open access), arxiv
  9. Ruzhansky M., Suragan D., Green’s identities, comparison principle and uniqueness of positive solutions for nonlinear p-sub-Laplacian equations on stratified Lie groups, Potential Analysis, to appear. arxiv, link
  10. Ruzhansky M., Sabitbek B., Suragan D., Hardy and Rellich inequalities for anisotropic p-sub-Laplacians, Banach J. Math. Anal., 14 (2020), 380-398. linkarxiv
  11. Kassymov A., Ruzhansky M., Suragan D., Fractional logarithmic inequalities and blow-up results with logarithmic nonlinearity on homogeneous groups. NoDEA Nonlinear Differential Equations Appl., 27 (2020), no. 1, Paper No. 7. link
  12. Ruzhansky M., Suragan D., Critical Hardy inequalities, Ann. Acad. Sci. Fenn. Math., 44 (2019), 1159-1174. link (download)arxiv
  13. Kassymov A., Ruzhansky M., Suragan D., Hardy-Littlewood-Sobolev and Stein-Weiss inequalities on homogeneous Lie groups. Integral Transforms and Special Functions, 30 (2019), 643-655. linkarxiv
  14. Ruzhansky M., Sabitbek B., Suragan D., Weighted anisotropic Hardy and Rellich type inequalities for general vector fields, NoDEA Nonlinear Differential Equations Appl., 26 (2019), no. 2, 26:13. linkarxiv
  15. Kalmenov T. Sh., Ruzhansky M., Suragan D., On spectral and boundary properties of the volume potential for the Helmholtz equation. Math. Model. Nat. Phenom., 14 (2019), no. 5, Art. 502, 11 pp. link
  16. Ozawa T., Ruzhansky M., Suragan D., Lp-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups, Quart. J. Math., 70 (2019), 305-318. arxiv, link, offprint (open access)
  17. Ruzhansky M., Sabitbek B., Suragan D., Weighted Lp-Hardy and Lp-Rellich inequalities with boundary terms on stratified Lie groups, Rev. Mat. Complutense, 32 (2019), 19-35. enhanced pdf (open access)arxiv, link
  18. Ruzhansky M., Suragan D., A note on stability of Hardy inequalitiesAnn. Funct. Anal., 9 (2018), 451-462. arxiv, link
  19. Ruzhansky M., Suragan D., A comparison principle for nonlinear heat Rockland operators on graded groups, Bull. Lond. Math. Soc., 50 (2018), 753-758. enhanced pdf (open access)arxiv, link
  20. Ruzhansky M., Suragan D., Elements of potential theory on Carnot groups, Funct. Anal. Appl., 52 (2018), 158-161. link(eng)link (rus)
  21. Ruzhansky M., Suragan D., Yessirkegenov N., Hardy-Littlewood, Bessel-Riesz, and fractional integral operators in anisotropic Morrey and Campanato spaces, Fract. Calc. Appl. Anal., 21 (2018), 577-612. arxiv, link
  22. Ruzhansky M., Suragan D., Yessirkegenov N., Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability and superweights for Lp-weighted Hardy inequalities, Trans. Amer. Math. Soc. Ser. B, 5 (2018), 32-62offprint (open access), link, arxiv
  23. Ruzhansky M., Suragan D., Yessirkegenov N., Sobolev type inequalities, Euler-Hilbert-Sobolev and Sobolev-Lorentz-Zygmund spaces on homogeneous groupsIntegral Equations Operator Theory, 90 (2018), no. 1, 90:10. enhanced pdf (open access)arxiv, link
  24. Ruzhansky M., Suragan D., Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups, Adv. Math., 317 (2017), 799-822. offprint (open access), arxiv, link
  25. Ruzhansky M., Suragan D., Anisotropic L2-weighted Hardy and L2-Caffarelli-Kohn-Nirenberg inequalities, Commun. Contemp. Math., 19 (2017), no. 6, 1750014, 12pp. offprint (open access), arxiv, link
  26. Ruzhansky M., Suragan D., Yessirkegenov N., Caffarelli-Kohn-Nirenberg and Sobolev type inequalities on stratified Lie groups, NoDEA Nonlinear Differential Equations Appl, 24 (2017), no. 5, 24:56. offprint (open access), arxiv, link
  27. Ruzhansky M., Suragan D., Geometric maximizers of Schatten norms of some convolution type integral operators, J. Math. Anal. Appl., 456 (2017), 444-456. arXivlink
  28. Ruzhansky M., Suragan D., Yessirkegenov N., Extended Caffarelli-Kohn-Nirenberg inequalities and superweights for Lp-weighted Hardy inequalities, C. R. Acad. Sci. Paris, 355 (2017), 694-698. offprint (open access), link
  29. Ruzhansky M., Suragan D., Uncertainty relations on nilpotent Lie groups, Proc. R. Soc. A, 473 (2017), no. 2201, 20170082, 12pp. offprint (open access), arxiv, link
  30. Ruzhansky M., Suragan D., Isoperimetric inequalities for some integral operators arising in potential theory, in Functional Analysis in Interdisciplinary Applications. FAIA 2017, 320-329, Springer Proceedings in Mathematics & Statistics, vol 216, Springer, 2017. arxivlink
  31. Ruzhansky M., Suragan D., Local Hardy and Rellich inequalities for sums of squares of vector fields, Adv. Diff. Equations, 22 (2017), 505-540. arxiv, link
  32. Garofalo N., Ruzhansky M., Suragan D., On Green functions for Dirichlet sub-Laplacians on H-type groups, J. Math. Anal. Appl., 452 (2017), 896-905. offprint (open access), link, arxiv
  33. Ruzhansky M., Suragan D., Layer potentials, Green formulae, Kac problem, and refined Hardy inequality on homogeneous Carnot groups, Adv. Math., 308 (2017), 483-528. offprint (open access), arxiv, link
  34. Ruzhansky M., Suragan D., On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and p-sub-Laplacian inequalities on stratified groups, J. Differential Equations, 262 (2017), 1799-1821. offprint (open access), arxiv, link
  35. Ruzhansky M., Suragan D., On first and second eigenvalues of Riesz transforms in spherical and hyperbolic geometries, Bull. Math. Sci., 6 (2016), 325-334. offprint (open access), arxiv, link
  36. Rozenblum G., Ruzhansky M., Suragan D., Isoperimetric inequalities for Schatten norms of Riesz potentials, J. Funct. Anal., 271 (2016), 224-239. offprint (open access), arxiv, link
  37. Ruzhansky M., Suragan D., On Schatten norms of convolution-type integral operators, Russ. Math. Surv., 71 (2016),157-158link
  38. Ruzhansky M., Suragan D., On Kac principle of not feeling the boundary for the Kohn Laplacian on the Heisenberg group, Proc. Amer. Math. Soc., 144 (2016), 709-721. arxiv, link
  39. Ruzhansky M., Suragan D., Isoperimetric inequalities for the logarithmic potential operator, J. Math. Anal. Appl.,434 (2016), 1676-1689. offprint (open access), arxiv, link

20190607_211942

20190607_212008

pde_group_final_small

Dr Erkinjon Karimov on State TV

 

Screen Shot 2019-12-27 at 5.58.37 PM

Dr Erkinjon Karimov, a long-term collaborator and an associated member of our Ghent Analysis & PDE Center was on the Uzbekistan State TV, celebrated for his scientific achievements. A special program was filmed about him.

Congratulations, Erkinjon!

Erkinjon has been our long-term visitor in 2019, and is planning to join us as a researcher from Autumn 2020, in the framework of our Odysseus project.

Erkinjon has just co-organised the Fractional Calculus Workshop with us.

Watch the YouTube Video (in Russian):

Erkin on TV

Forthcoming workshop Fractional Calculus, 9-10 June 2020

Workshop: Fractional Calculus

pde_slogan_black

International Workshop on Fractional Calculus

9-10 June 2020

Ghent Analysis & PDE Center

Ghent University/ZOOM

Add Conference to Google Calendar

ZOOM instructions (updated)

For the convenience of participants, if you want to obtain the zoom address of the meeting (before or during the conference), please send an email to Berikbol Torebek at berikbol.torebek@ugent.be

You can send it any time before or during the workshop. Once we have your interest and email address, we will send you the updated zoom link.

Book of Abstracts VIDEO

Description

The aim of the workshop is to exchange the recent progress and ideas in the field of fractional calculus and fractional differential equations (FDEs), and their applications to a variety of concrete problems. Our group took an initiative to organise this workshop for the continuity of research in the field despite the coronovirus times, therefore, the conference will take place on ZOOM.

The work of our group on the fractional calculus can be seen here

pde_group_final_small

There is also a forthcoming special issue on evolution equations with singularities.

pde_slogan_white

Confirmed Speakers

Workshop: Fractional Calculus, see details