Our updated research pages

We would like to share our update on the research pages: Functional inequalities and Nonharmonic analysis.

Functional inequalities: Here we present a historical overview of original Hardy inequality.

G. H. Hardy and Harald Bohr (pictures from Wikipedia)

G. H. Hardy reported Harald Bohr as saying ’all analysts spend half their time hunting through the literature for inequalities which they want to use but cannot prove’.

Nonharmonic analysis: We show the difference between harmonic vs nonharmonic analysis and give a survey of our recent works.

Harmonic analysis: symmetries in the underlying space, e.g. working with e^{2\pi i x\cdot\xi} on \mathbb T^n with \xi\in\mathbb Z^n; more generally, working with representations of compact, nilpotent, or more general locally compact type I groups;

Nonharmonic analysis: no symmetries in the underlying space, e.g. working with e^{2\pi i x\cdot\xi} on \mathbb T^n with \xi\not\in\mathbb Z^n; This name was given by Paley and Wiener.

A survey of our recent works on nonharmonic analysis

Prof. Ruzhansky gave a talk about “Nonharmonic pseudo-differential analysis” at Seminar on Analysis, Differential Equations and Mathematical Physics, at the Southern Federal University, Russia.

Our page about Nonharmonic analysis.


Here we break a talk to timestamps:

  • Overview of global (harmonic) quantization theories – 1:27
  • Harmonic analysis of pseudo-differential operators – 3:39
  • Harmonic vs nonharmonic analysis – 8:02
  • Nonharmonic analysis of boundary value problems – 11:23
  • General philosophy – 14:24
  • Global Fourier analysis associated to L and L* – 22:58
  • Convolution associated to L and L* – 27:52
  • Fourier multipliers – 36:06
  • Difference operators – 40:53
  • Summary of results – 52:32

    Interesting comments from Prof Lars-Erik Persson – The Happy Mathematician  55:30

Our Methusalem/Odysseus Programme on ResearchGate

Dear Colleagues,

ResearchGate is a European commercial social networking site for scientists and researchers to share papers, ask and answer questions, and find collaborators. By some people, it is also considered like a Facebook for scientists.

So we have created a ResearchGate page for our Methusalem/Odysseus Programme to advertise and share our research papers and related activities (conferences, posters, advertisements, etc.)

Congratulations to BMS with 100 years

Our group would like to congratulate the Belgian Mathematical Society (BMS) with 100 years anniversary since the BMS was founded on 14 March 1921. Surprisingly or not, this date coincides with the Pi-day (3.14) in Mathematics. Read more

BMS logo

Some highlights from the BMS Newsletter:

Congratulations to Leo Storme for being awarded a very prestigious Francqui chair at VUB 2021!

Come to Professor Storme inaugural lecture “FINITE GEOMETRY: PURE MATHEMATICS CLOSE TO PRACTICAL APPLICATIONS” on ZOOM on Monday, 19 April, 2021 – 18:00

Also, you find the information about our new junior seminar in the BMS newsletter, as well as an announcement of open positions at our Analysis & PDE Centre.

Happy Pi-day everyone!


We would like to recommend the Colloquia, Seminars and Lectures by METHUSALEM PROJECT PURE MATHEMATICS from KU Leuven.


The Methusalem colloquia are intended for a broad audience of graduate and PhD students, postdocs and professors. The series will include colloquia from guests as well as the first colloquium-style talk of the Methusalem Lecture Series. See more


The Junior Seminar in Pure Mathematics is an interdisciplinary seminar run by PhD students and postdocs at KU Leuven. The seminar is currently running online and hosts a 1-hour talk each session. See more


The Methusalem Lecture Series are mini-courses directed towards a broad audience of graduate students, PhD students, postdoctoral researches and professors. Each mini-course will start with a colloquium-style talk intended to be both accessible and attractive to mathematicians from diverse areas and will continue with a series of 3 to 5 lectures spanning 2 hours each. See more


New Ghent Methusalem Junior Analysis & PDE seminar

The Ghent Analysis & PDE Center is launching a new junior seminar:

Methusalem Junior Analysis & PDE Seminar is run by PhD students and postdocs at Ghent Analysis & PDE Center. It provides an opportunity to young researchers in various areas of analysis and PDEs to share their ideas and to learn new exciting things related to the topics of Analysis & PDEs as well as broader mathematical subjects.

All are welcome to attend!

The seminar currently takes place on ZOOM.

Website of the seminar

Congratulations to Prof Sadybekov and Dr Suragan for winning Kazakhstan State Prize

Kassym-Jomart Tokayev, President of Kazakhstan, signed a decree on awarding the State Prize in the field of science and technology named after al-Farabi to Prof Sadybekov and Dr Suragan for the series of works on “On the theory of nonlocal differential operators”.

This is the biggest scientific award in Kazakhstan, so congratulations!

We know both of them well, for example, from the cooperation on the just published (open access) book:

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

Spectral geometry of partial differential operators
Hardy inequalities on homogeneous groups

Many of us remember Durvudkhan’s visit to our Analysis & PDE group at UGent.

You can read more here on his achievements

Also, our PhD student Aishabibi Dukenbayeva is supervised jointly with Makhmud Sadybekov.

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