# Pseudo-Differential Conference

### ZOOM instructions

Speakers and colleagues with whom we have been in contact will receive individual zoom invitations. If you want to have full participating privileges (camera, microphone), please let us know. We can also upgrade your participation mode during the event, if you let us know via chat.

Join it as a webinar at

The start is at 10am CET (Central European Time)

# Video of Talks

## Description

The aim of the conference is to exchange the recent progress and ideas in the field of pseudo-differential operators and related broader analysis. Our group took an initiative to organise this workshop for the continuity of research in the field despite the coronavirus times, therefore, the conference will take place on ZOOM.

The conference will be of interest to all pseudo-differentiators, microlocalisers, and Fourier transformers, as well as to mathematicians working in related areas of analysis (noncommutative, spectral, harmonic, nonharmonic) and partial differential equations.

## Presenting a Poster

If you would like to present a poster at the conference, we are happy to do it. We may display it during some break, and will also put it on this website. If you are interested, let us know, and send your poster to the email address pseudodiff-conf@ugent.be

Michael Ruzhansky and Durvudkhan Suragan: Hardy inequalities on homogeneous groups

(thanks to Dr Bolys Sabitbek for making this poster)

Michael Ruzhansky, Makhmud Sadybekov and Durvudkhan Suragan: Spectral geometry of partial differential operators

(thanks to Dr Bolys Sabitbek for making this poster)

David Rottensteiner: The Harmonic Oscillator on The Heisenberg Group (Video)

Berikbol T. Torebek: Van der Corput lemmas for Mittag-Leffler functions

Jonas Brinker and Jens Wirth: Gelfand triples for the Kohn-Nirenberg quantization on a homogeneous Lie group

Arash Ghaani Farashahi and Gregory S. Chirikjian: Noncommutative Fourier Series on Γ\SE(2)

Marianna Chatzakou: On a class of anharmonic oscillators

Rakesh Kumar Parmar: Generalized Horn’s double Hypergeometric Function and Associated Properties

Mohammed Sebih: Weak solutions vs Strong Singularities

#### Pseudo-differentiators in Ghent

One definition of a pseudo-differential operator can be seen here

## Contact

And thanks to Duván and Marianna for making the book of abstracts!

## Some of our works in different settings:

#### Pseudo-differential operators on the torus Tn

Ruzhansky M., Turunen V., Quantization of pseudo-differential operators on the torus, J. Fourier Anal. Appl., 16 (2010), 943-982arxiv, link

#### Pseudo-differential operators on compact Lie groups

Ruzhansky M., Turunen V., Pseudo-differential Operators and Symmetries: Background Analysis and Advanced Topics, Birkhauser, Basel, 2010. 724pp. Contentsdescription and samplesthis book and time-frequency analysissummary at Birkhauser review Bookmetrix

#### Pseudo-differential operators on graded Lie groups

Fischer V., Ruzhansky M., Quantization on nilpotent Lie groups, Progress in Mathematics, Vol. 314, Birkhauser, 2016. xiii+557pp. linkdownload (open access bookfirst by Imperial College LondonBookmetrix the winner of  Ferran Sunyer I Balaguer Prize 2014

#### Pseudo-differential operators on Type I locally compact groups

Mantoiu M., Ruzhansky M., Pseudo-differential operators, Wigner transform and Weyl systems on type I locally compact groupsDoc. Math., 22 (2017), 1539-1592. offprint (open access)linkarxiv

#### Pseudo-differential operators on nilpotent Lie groups with flat orbits

Mantoiu M., Ruzhansky M., Quantizations on nilpotent Lie groups and algebras having flat coadjoint orbits. J. Geom. Anal., 29 (2019), 2823-2861. arxivlink

#### Pseudo-differential operators on manifolds (with boundaries)

1. Ruzhansky M., Tokmagambetov N., Nonharmonic analysis of boundary value problems, Int. Math. Res. Notices, (2016) 2016 (12), 3548-3615. offprint (open access)arxivlink
2. Ruzhansky M., Tokmagambetov N., Nonharmonic analysis of boundary value problems without WZ condition, Math. Model. Nat. Phenom.12 (2017), 115-140. arxivlink
3. Delgado J., Ruzhansky M., Tokmagambetov N., Schatten classes, nuclearity and nonharmonic analysis on compact manifolds with boundary, J. Math. Pures Appl.,107 (2017), 758-783. offprint (open access)arxivlink
4. Delgado J., Ruzhansky M., Fourier multipliers, symbols and nuclearity on compact manifolds, J. Anal. Math., 135 (2018), 757-800. offprint (open access)arxiv, link
5. Cardona D., Kumar V., Ruzhansky M., Tokmagambetov N., LpLq boundedness of pseudo-differential operators on smooth manifolds and its applications to nonlinear equationsarxiv

#### Pseudo-differential operators on the lattice Zn

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

In 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?

#### Pseudo-differential operators on locally compact and quantum groups

1. Akylzhanov R., Ruzhansky M., Lp-Lq multipliers on locally compact groups, J. Funct. Anal., 278 (2020), no. 3, 108324, 49pp. link (open access)arxiv
2. Akylzhanov R., Majid S., Ruzhansky M., Smooth dense subalgebras and Fourier multipliers on compact quantum groups, Comm. Math. Phys., 362 (2018), 761-799. offprint (open access), linkarxiv

#### Pseudo-differential operators with nonlinear quantizing functions

Esposito M., Ruzhansky M., Pseudo-differential operators with nonlinear quantizing  functions, Proc. Roy. Soc. Edinburgh Sect. A, 150 (2020), 103-130. arxiv, link

## Some other forthcoming conferences:

Generalised Functions Conference GF2020

Official GF2020 website

## Other possibly interesting/useful things:

1. Fischer V., Ruzhansky M., Quantization on nilpotent Lie groups, Progress in Mathematics, Vol. 314, Birkhauser, 2016. xiii+557pp. linkdownload (open access book, first by Imperial College London) Bookmetrix the winner of  Ferran Sunyer I Balaguer Prize 2014
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), 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)

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

If you work in analysis, there is still a possibility to submit a paper to the (refereed) volume: Ashyralyev A., Kalmenov T., Ruzhansky M., Sadybekov M., Suragan D. (Eds.) Functional Analysis in Interdisciplinary Applications II, Springer Proceedings in Mathematics & Statistics, Springer, to appear

#### Our modelling of COVID-19 for Belgium:

The effectiveness analysis is carried our for the lockdown in Belgium and of its duration, as well as of several phases of its relaxation. The comparative projection is made of different scenarios depending on the strength of confinement measures and their implementation.

Ruzhansky M., Tokmagambetov N., Torebek B., A projection model of COVID-19 pandemic for BelgiummedRxivpaper

## Posters

Many thanks to Dr Bolys Sabitbek for making this webpage.