# ProfessorMichaelRuzhansky

Faculty of Natural SciencesDepartment of Mathematics

Visiting Professor

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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
to

187 results found

Ruzhansky M, Suragan D, 2018, A NOTE ON STABILITY OF HARDY INEQUALITIES, ANNALS OF FUNCTIONAL ANALYSIS, Vol: 9, Pages: 451-462, ISSN: 2008-8752

JOURNAL ARTICLE

Ruzhansky M, Suragan D, 2018, A comparison principle for nonlinear heat Rockland operators on graded groups, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, Vol: 50, Pages: 753-758, ISSN: 0024-6093

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

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

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, Sabitbek B, Suragan D, Weighted $L^p$-Hardy and $L^p$-Rellich inequalities with boundary terms on stratified Lie groups, Revista Matemática Complutense, ISSN: 1139-1138

In this paper, generalised weighted $L^p$-Hardy,$L^p$-Caffarelli-Kohn-Nirenberg, and $L^p$-Rellich inequalities with boundaryterms are obtained on stratified Lie groups. As consequences, most of the Hardytype inequalities and Heisenberg- Pauli-Weyl type uncertainty principles onstratified groups are recovered. Moreover, a weighted $L^2$-Rellich typeinequality with the boundary term is obtained.

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

Dasgupta A, Ruzhansky M, 2018, Eigenfunction expansions of ultradifferentiable functions and ultradistributions. II. Tensor representations, Transactions of the American Mathematical Society, Series B, Vol: 5, Pages: 81-101, ISSN: 0002-9947

In this paper we analyse the structure of the spaces of coefficients ofeigenfunction expansions of functions in Komatsu classes on compact manifolds,continuing the research in our previous paper. We prove that such spaces ofFourier coefficients are perfect sequence spaces. As a consequence we describethe tensor structure of sequential mappings on spaces of Fourier coefficientsand characterise their adjoint mappings. In particular, the considered classesinclude spaces of analytic and Gevrey functions, as well as spaces ofultradistributions, yielding tensor representations for linear mappings betweenthese spaces on compact manifolds.

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

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

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

Delgado J, Ruzhansky M, 2018, THE BOUNDED APPROXIMATION PROPERTY OF VARIABLE LEBESGUE SPACES AND NUCLEARITY, MATHEMATICA SCANDINAVICA, Vol: 122, Pages: 299-319, ISSN: 0025-5521

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

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, Tokmagambetov N, 2017, Wave Equation for Operators with Discrete Spectrum and Irregular Propagation Speed, ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, Vol: 226, Pages: 1161-1207, ISSN: 0003-9527

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

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

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, 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

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

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

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

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

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

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

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

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

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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