Summary for 2019

The year 2019 was exciting as this was the first full year of functioning of our new Odysseus Analysis & PDE group at UGent. Here we try to summarise the main highlights from this year.

Prizes/Awards and Grants:

  • Ferran Sunyer i Balaguer Prize to the book “Hardy inequalities on homogeneous groups” by M. Ruzhansky and D. Suragan
  • Marie Curie Project to Serena Federico
  • London Mathematical Society Early Career Fellowship to Nurgissa Yessirkegenov
  • Two CSC grants to Qing Hong and Guorong Hu for 1-year visits to Ghent Analysis & PDE
  • Stipend for talented young scientists by the Kazakhstan Government to Aidyn Kassymov
  • 8th European Congress of Mathematics scholarship to Bolys Sabitbek
  • BOF starting grant to Michael Ruzhansky
  • Flemish Government Doctoral School grant for “Inverse Spectral and Scattering Problems”

Securing the following large international conferences to be organised by our group at UGent:

  • GF2020 International Conference on Generalized Functions, 31 August – 4 September 2020, at Ghent University, Belgium
  • 13th ISAAC Congress, to take place 2-6 August, 2021, at Ghent University, Belgium
  • Computability in Europe 2021, to take place 5-9 July, 2021, at Ghent University, Belgium

PhD students (defended in 2019 and new)
In particular, 12 new PhD students are starting at UGent, supervised by Michael Ruzhansky 

newMohammed Sebih (Ghent University)
newTimur Merembayev (Ghent University and International University of Information Technologies)
newAigul Satybaldina (Ghent University and Eurasian National University)
newJuan Pablo Velasquez Rodriguez, Ghent University
newDuvan Cardona, Ghent University
newJunqing Huang, Ghent University
newMarkos Fisseha Yimer (Addis Ababa University)
newBayan Bekbolat (Ghent University and Kazakh National University)
newDaurenbek Serikbaev (Ghent University and Kazakh National University)
newAishabibi Dukenbayeva (Ghent University and Kazakh National University)
newArshyn Altybay (Ghent University and Kazakh National University), PhD in Computer Science
newAtile Nega (Ghent University and Addis Ababa University)
currentMarianna Chatzakou, Imperial College London
newAidyn Kassymov (Ghent University and Kazakh National University)
PhD defended January 2020Nurgissa Yessirkegenov, Function spaces on Lie groups and applications, Imperial College London
PhD defended December 2019Thomas Baker, Short time pseudo-differential operators, Imperial College London
PhD awarded 2019Bolys Sabitbek, Hardy-Sobolev type inequalities on homogeneous groups and applications (co-advisor M. Ruzhansky UGent, Kazakh National University)
PhD awarded 2019Massimiliano Esposito, Non linear τ quantizing functions and a version of the Weyl quantization on Zn, Imperial College London

Our Analysis & PDE group has initiated the joint PhD agreements of UGent with:

  1. Kazakh National University, Kazakhstan
  2. Eurasian National University, Kazakhstan
  3. Addis Ababa University, Ethiopia
  4. International University of Information Technologies, Kazakhstan
  5. North-Eastern Federal University, Yakutsk, Russia
  6. Djillali Liabes University of Sidi Bel Abbes, Algeria

Our Analysis & PDE group has initiated the following research collaborations with applications of our expertise in Mathematics:

  1. Research collaboration with Beijing University of Aeronautics and Astronautics (BUAA), China, on image processing (car number plates recognition, segmentation, endoscopy video enhancement, illumination correction, etc.)
  2. Research collaboration with North-Eastern Federal University, Yakutsk, Russia, on image processing and deep learning for medical diagnosis (analysis of blood cells and the attached nanoparticles)
  3. Research collaboration in colour imaging with UGent TELIN group on colour enhancement in image illumination problems
  4. Cooperation with VUB on digital mathematics and noncommutative analysis

For some details see our Medical Imaging & Analysis page.

Publications:

(for exact links for publications see the websites of respective members)

  1. Botchway L., Kibiti G., Ruzhansky M., Difference equations and pseudo-differential operators on Zn, J. Funct. Anal., to appear.
  2. Kassymov A., Ruzhansky M., Suragan D., Fractional logarithmic inequalities and blow-up results with logarithmic nonlinearity on homogeneous groups. NoDEA Nonlinear Differential Equations Appl., to appear.
  3. Ruzhansky M., Yessirkegenov N., Very weak solutions to hypoelliptic wave equations. J. Differential Equations, to appear.
  4. Ruzhansky M., Sabitbek B., Suragan D., Hardy and Rellich inequalities for anisotropic p-sub-Laplacians, and horizontal Hardy inequalities for multiple singularities and multi-particles on stratified groups, Banach Journal of Mathematical Analysis, to appear
  5. Esposito M., Ruzhansky M., Pseudo-differential operators with nonlinear quantizing functions, Proc. Roy. Soc. Edinburgh Sect. A, to appear
  6. 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
  7. Ruzhansky M., Yessirkegenov N., Factorizations and Hardy-Rellich inequalities on stratified groups, J. Spectr. Theory, to appear
  8. Akylzhanov R., Ruzhansky M., Lp-Lq multipliers on locally compact groups, J. Funct. Anal., 278 (2020), 108324. link (open access)
  9. Ruzhansky M., Tokmagambetov N., Torebek B., Bitsadze-Samarskii type problem for the integer-differential diffusion-wave equation on the Heisenberg group, Integral Transforms and Special Functions, 31 (2020), 1-9. link (open access)
  10. Ruzhansky M., Tokmagambetov N., Torebek B., Inverse source problems for positive operators. I: Hypoelliptic diffusion and subdiffusion equations. Journal of Inverse and Ill-Posed Problems, 27 (2019), 891-911. link, arxiv
  11. Altybay A., Ruzhansky M., Tokmagambetov N., Wave equation with distributional propagation speed and mass term: numerical simulations. Appl. Math. E-Notes, 19 (2019), 552-562. free download
  12. Laptev A., Ruzhansky M., Yessirkegenov N., Hardy inequalities for Landau Hamiltonian and for Baouendi-Grushin operator with Aharonov-Bohm type magnetic field. Part I. Math. Scand., 125 (2019), 239-269. link, arxiv
  13. Ruzhansky M., Yessirkegenov N., Limiting cases of Sobolev inequalities on stratified groups. Proc. Japan. Acad. Ser. A. Math. Sci., 95 (2019), 83-87. link
  14. Akylzhanov R., Nursultanov E., Ruzhansky M., Hardy-Littlewood, Hausdorff-Young-Paley inequalities, and Lp-Lq Fourier multipliers on compact homogeneous manifolds, J. Math. Anal. Appl., 479 (2019), 1519-1548. arxiv, link
  15. Munoz J. C., Ruzhansky M., Tokmagambetov N.,  Acoustic and shallow water wave propagations with irregular dissipation, Funct. Anal. Appl., 53 (2019), 153-156. link, view paper
  16. Ruzhansky M., Suragan D., Critical Hardy inequalities, Ann. Acad. Sci. Fenn. Math., 44 (2019), 1159-1174. link (download), arxiv
  17. Mantoiu M., Ruzhansky M., Quantizations on nilpotent Lie groups and algebras having flat coadjoint orbits. J. Geom. Anal., 29 (2019), 2823-2861. arxiv, link
  18. Huang J., Ruzhansky M., Feng H., Zheng L., Huang X., Wang H., Feature extraction for license plate location based on L0-norm smoothing. Open Comput. Sci. 2019; 9:28-135. link (open access)
  19. 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. link, arxiv
  20. Daher R., Delgado J., Ruzhansky M., Titchmarsh theorems for Fourier transforms of Holder-Lipschitz functions on compact homogeneous manifolds, Monatsh. Math., 189 (2019), 23-49. arxiv, link (open access)
  21. Ruzhansky M., Tokmagambetov N., On nonlinear damped wave equations for positive operators. I. Discrete spectrum. Differential Integral Equations, 32 (2019), 455-478. link, arxiv
  22. Matsuyama T., Ruzhansky M., On the Gevrey well-posedness of the Kirchhoff equation. J. Anal. Math., 137 (2019), 449-468. link, arxiv, paper
  23. Delgado J., Ruzhansky M., Lp-bounds for pseudo-differential operators on compact Lie groups. J. Inst. Math. Jussieu, 18 (2019), 531–559. offprint (open access), arxiv, link
  24. 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. link, arxiv
  25. 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
  26. 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),
  27. Ruzhansky M., Verma D., Hardy inequalities on metric measure spaces, Proc. R. Soc. A, 475 (2019), 20180310, 15pp. offprint, arxiv, link
  28. Ruzhansky M., Tokmagambetov N., Wave equation for 2D Landau Hamiltonian,  Appl. Comput. Math., 18 (2019), 69-78. arxiv
  29. Munoz J. C., Ruzhansky M., Tokmagambetov N., Wave propagation with irregular dissipation and applications to acoustic problems and shallow waters. J. Math. Pures Appl., 123 (2019), 127-147. offprint (open access), arxiv, link
  30. Ruzhansky M., Sugimoto M., A local-to-global boundedness argument and Fourier integral operators, J. Math. Anal. Appl., 473 (2019), 892-904
  31. 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
  32. Ruzhansky M., Yessirkegenov N., Rellich inequalities for sub-Laplacians with drift, Proc. Amer. Math. Soc., 147 (2019), 1335-1349. arxiv, link
  33. S. S. Darogomir, B. T. Torebek, Some Hermite-Hadamard type inequalities in the class of hyperbolic p-convex functions. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 113:4 (2019), 3413–3423
  34. B. T. Torebek, Global Unsolvability of the Burgers Equation with Fractional Time Derivative. Differential Equations, 55:6 (2019), 867–870
  35. M. Kirane, B. T. Torebek, Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations. Fractional Calculus and Applied Analysis, 22:2 (2019), 358–378
  36. B. Ahmad, A. Alsaedi, M. Kirane, B. T. Torebek, Hermite-Hadamard, Hermite-Hadamard-Fejer, Dragomir-Agarwal and Pachpatte type inequalities for convex functions via new fractional integrals, Journal of Computational and Applied Mathematics, 353 (2019), 120–129
  37. N. Al-Salti, M. Kirane, B. T. Torebek, On a class of inverse problems for a heat equation with involution perturbation. Hacettepe Journal of Mathematics and Statistics, 48:3 (2019), 669–681
  38. T. Sh. Kalmenov, B. T. Torebek, A method for solving ill-posed nonlocal problem for the elliptic equation with data on the whole boundary, Journal of Pseudo-Differential Operators and Applications, 10:1 (2019), 177–185
  39. T. Sh. Kalmenov, M. A. Sadybekov, B. T. Torebek, A criterion of solvability of the elliptic Cauchy problem in a multi-dimensional cylindrical domain, Complex Variables and Elliptic Equations, 64:3 (2019), 398–408
  40. Vishvesh Kumar, Orlicz spaces and amenability of hypergroups, Bull. Ira. Math. Soc. (2019). DOI: https://doi.org/10.1007/s41980-019-00310-7
  41. Vishvesh Kumar and Ritumoni Sarma, Hausdorff-Young inequality for Orlicz spaces on compact  hypergroups, (to appear in) Colloquium Mathematicum, (2019).
  42. Vishvesh Kumar and N. Shravan Kumar, Vector-valued Fourier analysis on hypergroups, (to appear in) Operator and Matrices (2019).
  43. Vishvesh Kumar, Shravan Kumar, and Ritumoni Sarma, Unbounded translation invariant operators on commutative hypergroups, (to appear in) Methods of Functional analysis and Topology, (2019).
  44. Vishvesh Kumar, Shravan Kumar, and Ritumoni Sarma, Characterization of multipliers on hypergroups, (to appear in) Acta Mathematica Vietnamica, (2019).
  45. Duvan Cardona and Vishvesh Kumar, L^p-boundedness and L^p-nuclearity of multilinear pseudo-differential operators on Z^nand the torus T^n , Journal of Fourier analysis and applications (2019)   DOI: 10.1007/s00041-019-09689-7
  46. Vishvesh Kumar and M. W. Wong, C*-algebra, H*-algebra and trace ideals of pseudo-differential operators on locally compact, Hausdorff and abelian groups, Journal of Pseudo differential operators and applications, 10(2) 269-283 (2019).
  47. Vishvesh Kumar, Pseudo-differential operators on homogeneous spaces of compact and Hausdorff groups, Forum Mathematicum, 31(2) 275-282 (2019).
  48. Vishvesh Kumar, Kenneth A. Ross, and Ajit Iqbal Singh, Hypergroup deformations of semigroups, Semigroup Forum, 99(1) 169-195 (2019). 
  49. Vishvesh Kumar, Kenneth A. Ross, and Ajit Iqbal Singh, An addendum to “Hypergroup deformations of semigroups,” Semigroup Forum, 99(1) 196-197 (2019).
  50. Vishvesh Kumar, Kenneth A. Ross, and Ajit Iqbal Singh, Ramsey theory for hypergroups, Semigroup Forum,(2019). DOI: https://doi.org/10.1007/s00233-019-10009-
  51. Vishvesh Kumar, R. Sarma, and N. Shravan Kumar, Orlicz spaces on hypergroups, Publications MathematicaeDebrecen, 94(1-2) 31–47 (2019).
  52. Lj. Oparnica, E. Süli, Well-posedness of the fractional Zener wave equation for heterogenous viscoelastic materials, accepted for the publication in Fractional Calculus and Applied Analysis
  53. Lj. Oparnica, D. Zorica, and A. Okuka. Fractional Burgers wave equation, Acta Mechanica, 230(12), 4321-4340, 2019.
  54. T. M. Atanackovic, Ljubica Oparnica, and Dusan Zorica, Bifurcation analysis of rotating axially compressed imperfect nano-rod. ZAMM, Z. Angew. Math. Mech. DOI: 10.1002/zamm.201800284, 2019.
  55. S. Konjik, Lj. Oparnica, and D. Zorica. Distributed-order fractional constitutive stress-strain relation in wave propagation modeling. Zeitschrift für angewandte Mathematik und Physik, 70:51, 2019.
  56. M.А. Sadybekov, A.A. Dukenbayeva, Direct and inverse problems for the Poisson equation with equality of flows on a part of the boundary, Complex Variables and Elliptic Equations, 64(5):777-791, 2019.
  57. Hasanov, A. S. Berdyshev and A. R. Ryskan. Fundamental solutions for a class of four-dimensional degenerate elliptic equation. Complex variables and elliptic equations.  https://doi.org/10.1080/17476933.2019.1606803
  58. Berdyshev A.S., Hasanov A. Ergashev T.G. Double-layer potentials for generalized bi-axially symmetric Helmholtz equation II. Complex variables and elliptic equations. https:/doi.org/10.1080/17476933.2019.1583219
  59. Hasanov A., Ergashev T.G. Analytical continuation formulas for Lauricella hypergeometric functions in three variables. Bulletin of the Institute of Mathematics, – V. 5, (2019), 50-59.
  60. Hasanov A., Ruzhansky M., Euler-type integral representations for the hypergeometric functions in three variables of second order, Bulletin of the Institute of Mathematics, 2019: 6, 73-223.
  62. M. Ruzhansky, B. Sabitbek, D. Suragan, Principal frequency of p-versions of sub Laplacian for general vector fields, preprint 2019, submitted.
  63. Kassymov A., Ruzhansky M., Suragan D., Reverse Stein-Weiss, Hardy-Littlewood-Sobolev, Hardy, Sobolev and Caffarelli-Kohn-Nirenberg inequalities on homogeneous groups, arxiv
  64. Kassymov A., Ruzhansky M., Suragan D., Reverse integral Hardy inequalities on metric measure spaces. arxiv
  65. Kumar V., Ruzhansky M., Hausdorff-Young inequality for Orlicz spaces on compact homogeneous manifolds. arxiv
  66. Cardona D., Delgado J., Ruzhansky M., Lp-bounds for pseudo-differential operators on graded Lie groups. arxiv
  67. Kirilov A., De Moraes W., Ruzhansky M., Global properties of vector fields on compact Lie groups in Komatsu classes. II. Normal forms. arxiv
  68. Kirilov A., De Moraes W., Ruzhansky M., Global properties of vector fields on compact Lie groups in Komatsu classes. arxiv
  69. Kirilov A., De Moraes W., Ruzhansky M., Global hypoellipticity and global solvability for vector fields on compact Lie groups. arxiv
  70. Kirilov A., De Moraes W., Ruzhansky M., Partial Fourier series on compact Lie groups. arxiv
  71. Akylzhanov R., Liflyand E., Ruzhansky M., Re-expansions on compact Lie groups. arxiv
  72. Ruzhansky M., Velasquez-Rodriguez J. P., Non-harmonic Gohberg’s lemma, Gershgorin theory and heat equation on manifolds with boundary. arxiv
  73. Ruzhansky M., Sabitbek B., Suragan D., Geometric Hardy inequalities on starshaped sets. arxiv
  74. Cardona D., Ruzhansky M., Boundedness of pseudo-differential operators in subelliptic Sobolev and Besov spaces on compact Lie groups. Arxiv
  75. Gröchenig, K., Romero José Luis, Rottensteiner, D., van Velthoven, J. T. Balian-Low type theorems on homogeneous groups
  76. Aparajita Dasgupta and Vishvesh Kumar, Ellipticity and Fredholmness of pseudo-differential operators on Zn, (submitted). arXiv link: https://arxiv.org/abs/1910.05582
  77. Aparajita Dasgupta and Vishvesh Kumar, Hilbert-Schmidt and trace class pseudo-differential operators on the abstract Heisenberg group,  (submitted). arXiv link: https://arxiv.org/abs/1902.09869   
  78. Duvan Cardona and Vishvesh Kumar, The nuclear trace of periodic pseudo-differential operators with applications to index theory, (submitted). arXiv link:   https://arxiv.org/abs/1901.10010    
  79. Vishvesh Kumar, Orlicz Modules over coset spaces of Compact subgroups in locally compact groups, (Submitted). arXiv link:  https://arxiv.org/abs/1905.05971
  80. Ibrahim Akbarbaglu, M. R. Azimi and Vishvesh Kumar, Topological transitive sequence of cosine operators on Orlicz spaces, (submitted). arXiv link:  https://arxiv.org/abs/1809.06085
  81. Huang, J., Ruzhansky M., Wang, H. (2020). Reliable weakly supervised photo enhancer with inexact training pairs.
  82. Sabitbek B. Weighted and logarithmic Caffarelli-Kohn-Nirenberg type inequalities on stratified groups and applications. Submitted.
  83. Zoric D., Oparnica Lj. Energy dissipation for hereditary and energy conservation for non-local fractional wave equations. arxiv
  84. Duvan Cardona, Cesar Del Correl and Vishvesh Kumar, Dixmier trace for discretepseudo-differential operators, (submitted). arXiv https://arxiv.org/abs/1911.03924
  85. Vishvesh Kumar and S. S. Mondal, Schatten Class and nuclear pseudo–differential operators on homogeneous spaces of compact group, (2019),  arXiv:1911.10554v1​
  86. A. Velicu and N. Yessirkegenov. Rellich, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg inequalities for Dunkl operators and applications.arXiv preprint arXiv:1904.08725 (2019).
  87. Mamaeva S.N., Kononova I.V., Ruzhansky M., Nikiforov P.V., Nikolaevа N.A., Pavlov A.N., Fedorova N.F., Huang J., Semenova M.N.,  Barashkova D.V., Frolova L.S., Maksimov G.V., Using Scanning Electron Microscopy and Atomic Force Microscopy to Study the Formation of Nanoparticles on Red Blood Cell Surface in Cervical Cancer Patients, International Journal of Biomedicine, awaiting publication