ProfessorMichaelRuzhansky

Faculty of Natural SciencesDepartment of Mathematics

Professor of Pure Mathematics

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Contact

+44 (0)20 7594 8500m.ruzhansky CV

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Location

615Huxley BuildingSouth Kensington Campus

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Publications

Publication Type
Year
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175 results found

Akylzhanov R, Majid S, Ruzhanskye M, 2018, Smooth Dense Subalgebras and Fourier Multipliers on Compact Quantum Groups, COMMUNICATIONS IN MATHEMATICAL PHYSICS, Vol: 362, Pages: 761-799, ISSN: 0010-3616

JOURNAL ARTICLE

Delgado J, Ruzhansky M, 2018, Fourier multipliers, symbols, and nuclearity on compact manifolds, JOURNAL D ANALYSE MATHEMATIQUE, Vol: 135, Pages: 757-800, ISSN: 0021-7670

JOURNAL ARTICLE

Garetto C, Jäh C, Ruzhansky M, 2018, Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, I. Well-posedness, Mathematische Annalen, ISSN: 0025-5831

In this paper we analyse the well-posedness of the Cauchy problem for arather general class of hyperbolic systems with space-time dependentcoefficients and with multiple characteristics of variable multiplicity. First,we establish a well-posedness result in anisotropic Sobolev spaces for systemswith upper triangular principal part under interesting natural conditions onthe orders of lower order terms below the diagonal. Namely, the terms below thediagonal at a distance $k$ to it must be of order $-k$. This setting alsoallows for the Jordan block structure in the system. Second, we give conditionsfor the Schur type triangularisation of general systems with variablecoefficients for reducing them to the form with an upper triangular principalpart for which the first result can be applied. We give explicit details forthe appearing conditions and constructions for $2\times 2$ and $3\times 3$systems, complemented by several examples.

JOURNAL ARTICLE

Ruzhansky M, Suragan D, Yessirkegenov N, 2018, Sobolev Type Inequalities, Euler-Hilbert-Sobolev and Sobolev-Lorentz-Zygmund Spaces on Homogeneous Groups, INTEGRAL EQUATIONS AND OPERATOR THEORY, Vol: 90, ISSN: 0378-620X

JOURNAL ARTICLE

Ruzhansky M, Tokmagambetov N, 2018, Nonlinear damped wave equations for the sub-Laplacian on the Heisenberg group and for Rockland operators on graded Lie groups, Journal of Differential Equations, ISSN: 0022-0396

In this paper we study the Cauchy problem for the semilinear damped wave equation for the sub-Laplacian on the Heisenberg group. In the case of the positive mass, we show the global in time well-posedness for small data for power like nonlinearities. We also obtain similar well-posedness results for the wave equations for Rockland operators on general graded Lie groups. In particular, this includes higher order operators on and on the Heisenberg group, such as powers of the Laplacian or the sub-Laplacian. In addition, we establish a new family of Gagliardo-Nirenberg inequalities on graded Lie groups that play a crucial role in the proof but which are also of interest on their own: if $G$ is a graded Lie group of homogeneous dimension $Q$ and $a>0$, $1<r<\frac{Q}{a},$ and $1\leq p\leq q\leq \frac{rQ}{Q-ar},$ then we have the following Gagliardo-Nirenberg type inequality $$\|u\|_{L^{q}(G)}\lesssim \|u\|_{\dot{L}_{a}^{r}(G)}^{s} \|u\|_{L^{p}(G)}^{1-s}$$ for $s=\left(\frac1p-\frac1q\right)\left(\frac{a}Q+\frac1p-\frac1r\right)^{-1}\in [0,1]$ provided that$\frac{a}Q+\frac1p-\frac1r\not=0$, where $\dot{L}_{a}^{r}$ is the homogeneous Sobolev space of order $a$ over $L^r$. If $\frac{a}Q+\frac1p-\frac1r=0$, we have $p=q=\frac{rQ}{Q-ar}$, and then the above inequality holds for any $0\leqs\leq 1$.

JOURNAL ARTICLE

Ruzhansky M, Tokmagambetov N, 2018, Convolution, Fourier analysis, and distributions generated by Riesz bases, MONATSHEFTE FUR MATHEMATIK, Vol: 187, Pages: 147-170, ISSN: 0026-9255

JOURNAL ARTICLE

Ruzhansky MV, Suragan D, 2018, Elements of Potential Theory on Carnot Groups, FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, Vol: 52, Pages: 158-161, ISSN: 0016-2663

JOURNAL ARTICLE

Ruzhansky MV, Tokmagambetov NE, 2018, On a Very Weak Solution of the Wave Equation for a Hamiltonian in a Singular Electromagnetic Field, MATHEMATICAL NOTES, Vol: 103, Pages: 856-858, ISSN: 0001-4346

JOURNAL ARTICLE

Akylzhanov R, Ruzhansky M, 2017, NET SPACES ON LATTICES, HARDY-LITTLEWOOD TYPE INEQUALITIES, AND THEIR CONVERSES, Publisher: L N GUMILYOV EURASIAN NATL UNIV

WORKING PAPER

Cardona D, Ruzhansky M, 2017, Multipliers for Besov spaces on graded Lie groups, COMPTES RENDUS MATHEMATIQUE, Vol: 355, Pages: 400-405, ISSN: 1631-073X

JOURNAL ARTICLE

Dasgupta A, Ruzhansky M, 2017, THE GOHBERG LEMMA, COMPACTNESS, AND ESSENTIAL SPECTRUM OF OPERATORS ON COMPACT LIE GROUPS (vol 128, pg 179, 2016), JOURNAL D ANALYSE MATHEMATIQUE, Vol: 132, Pages: 395-395, ISSN: 0021-7670

JOURNAL ARTICLE

Delgado J, Ruzhansky M, 2017, Schatten classes and traces on compact groups, MATHEMATICAL RESEARCH LETTERS, Vol: 24, Pages: 979-1003, ISSN: 1073-2780

JOURNAL ARTICLE

Delgado J, Ruzhansky M, 2017, -BOUNDS FOR PSEUDO-DIFFERENTIAL OPERATORS ON COMPACT LIE GROUPS, Journal of the Institute of Mathematics of Jussieu, Pages: 1-29, ISSN: 1474-7480

JOURNAL ARTICLE

Delgado J, Ruzhansky M, Tokmagambetov N, 2017, Schatten classes, nuclearity and nonharmonic analysis on compact manifolds with boundary, JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, Vol: 107, Pages: 758-783, ISSN: 0021-7824

JOURNAL ARTICLE

Garetto C, Ruzhansky M, 2017, On hyperbolic systems with time-dependent Holder characteristics, ANNALI DI MATEMATICA PURA ED APPLICATA, Vol: 196, Pages: 155-164, ISSN: 0373-3114

JOURNAL ARTICLE

Garetto C, Ruzhansky M, 2017, On C-infinity well-posedness of hyperbolic systems with multiplicities, ANNALI DI MATEMATICA PURA ED APPLICATA, Vol: 196, Pages: 1819-1834, ISSN: 0373-3114

JOURNAL ARTICLE

Garofalo N, Ruzhansky M, Suragan D, 2017, On Green functions for Dirichlet sub-Laplacians on H-type groups, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, Vol: 452, Pages: 896-905, ISSN: 0022-247X

JOURNAL ARTICLE

Kanguzhin B, Ruzhansky M, Tokmagambetov N, 2017, On convolutions in Hilbert spaces, FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, Vol: 51, Pages: 221-224, ISSN: 0016-2663

JOURNAL ARTICLE

Mantoiu M, Ruzhansky M, 2017, Pseudo-differential operators, Wigner transform and Weyl systems on type I locally compact groups, Documenta Mathematica, Vol: 22, Pages: 1539-1592, ISSN: 1431-0635

Let G be a unimodular type I second countable locally compactgroup and let Gb be its unitary dual. We introduce and study a globalpseudo-differential calculus for operator-valued symbols defined on G × Gb ,and its relations to suitably defined Wigner transforms and Weyl systems.We also unveil its connections with crossed products C∗-algebras associatedto certain C∗-dynamical systems, and apply it to the spectral analysisof covariant families of operators. Applications are given to nilpotentLie groups, in which case we relate quantizations with operator-valued andscalar-valued symbols.

JOURNAL ARTICLE

Matsuyama T, Ruzhansky M, 2017, Almost global well-posedness of Kirchhoff equation with Gevrey data, COMPTES RENDUS MATHEMATIQUE, Vol: 355, Pages: 522-525, ISSN: 1631-073X

JOURNAL ARTICLE

Matsuyama T, Ruzhansky M, 2017, The Kirchhoff Equation with Gevrey Data, 10th International Congress of the International-Society-for-Analysis-its-Applications-and-Computations (ISAAC), Publisher: BIRKHAUSER BOSTON, Pages: 313-318, ISSN: 2297-0215

CONFERENCE PAPER

Ruzhansky M, Agarwal P, Area I, Karimov ETet al., 2017, Preface for the Special Issueon "Special functions and analysis of PDEs", MATHEMATICAL MODELLING OF NATURAL PHENOMENA, Vol: 12, Pages: 1-3, ISSN: 0973-5348

JOURNAL ARTICLE

Ruzhansky M, Suragan D, 2017, Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups, Advances in Mathematics, Vol: 308, Pages: 483-528, ISSN: 1090-2082

We propose the analogues of boundary layer potentials for the sub-Laplacian on homogeneous Carnot groups/stratified Lie groups and prove continuity results for them. In particular, we show continuity of the single layer potential and establish the Plemelj type jump relations for the double layer potential. We prove sub-Laplacian adapted versions of the Stokes theorem as well as of Green's first and second formulae on homogeneous Carnot groups. Several applications to boundary value problems are given. As another consequence, we derive formulae for traces of the Newton potential for the sub-Laplacian to piecewise smooth surfaces. Using this we construct and study a nonlocal boundary value problem for the sub-Laplacian extending to the setting of the homogeneous Carnot groups M. Kac's “principle of not feeling the boundary”. We also obtain similar results for higher powers of the sub-Laplacian. Finally, as another application, we prove refined versions of Hardy's inequality and of the uncertainty principle.

JOURNAL ARTICLE

Ruzhansky M, Suragan D, 2017, Uncertainty relations on nilpotent Lie groups, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 473, ISSN: 1364-5021

JOURNAL ARTICLE

Ruzhansky M, Suragan D, 2017, Anisotropic L-2-weighted Hardy and L-2-Caffarelli-Kohn-Nirenberg inequalities, COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, Vol: 19, ISSN: 0219-1997

JOURNAL ARTICLE

Ruzhansky M, Suragan D, 2017, Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups, ADVANCES IN MATHEMATICS, Vol: 317, Pages: 799-822, ISSN: 0001-8708

JOURNAL ARTICLE

Ruzhansky M, Suragan D, 2017, Geometric maximizers of Schatten norms of some convolution type integral operators, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, Vol: 456, Pages: 444-456, ISSN: 0022-247X

JOURNAL ARTICLE

Ruzhansky M, Suragan D, Yessirkegenov N, 2017, Extended Caffarelli-Kohn-Nirenberg inequalities and superweights for L-p-weighted Hardy inequalities, COMPTES RENDUS MATHEMATIQUE, Vol: 355, Pages: 694-698, ISSN: 1631-073X

JOURNAL ARTICLE

Ruzhansky M, Suragan D, Yessirkegenov N, 2017, Caffarelli-Kohn-Nirenberg and Sobolev type inequalities on stratified Lie groups, NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, Vol: 24, ISSN: 1021-9722

JOURNAL ARTICLE

Ruzhansky M, Tokmagambetov N, 2017, Very weak solutions of wave equation for Landau Hamiltonian with irregular electromagnetic field, LETTERS IN MATHEMATICAL PHYSICS, Vol: 107, Pages: 591-618, ISSN: 0377-9017

JOURNAL ARTICLE

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