12 citations · 14 across the 18 of their papers we have counts for
19 papers
On a fractional nonlinear Schrödinger equation with irregular coefficients. case: d<2s
Arshyn Altyby, Michael Ruzhansky, Mohammed Elamine Sebih +1
In the case when , where is the space dimension and is the fractional power of the Laplacian, we study the well-posedness for a cubic nonlinear Schrödinger equation (…
Reproducing Kernel Hilbert Spaces and entropy Kolmogorov numbers on compact Lie Groups
Zhirayr Avetisyan, Michael Ruzhansky, Karina Gonzalez
On a compact Lie group , we consider the reproducing kernel Hilbert space associated with the integral kernel of a left-invariant, positive, symmetric, trace…
Functional calculus for Safarov pseudo-differential operators
Santiago Gómez Cobos, Michael Ruzhansky
Given a smooth, closed Riemannian manifold equipped with a linear connection (not necessarily metric), we develop the holomorphic functional calculus for operators…
A Closed-form Approximation for Impulse Response of Fractionally Damped Oscillators
Shashank Pathak, Michael Ruzhansky, Karel Van Bockstal
We consider a fractionally damped oscillator, where the damping term is expressed by the Caputo fractional derivative of order The impulse response of this oscillator…
Hardy-Hilbert type inequalities on homogeneous groups-An introduction and generalization to the kernel case
Markos Fisseha Yimer, Lars Erik Persson, Michael Ruzhansky +2
There is a lot of information available concerning Hardy-Hilbert type inequalities in one or more dimensions. In this paper we introduce the development of such inequalities on hom…
Levin-Cochran-Lee inequalities and best constants on homogeneous groups
Michael Ruzhansky, Markos Fisseha Yimer
In this paper, we apply a direct method instead of a limit approach, for proving the Levin-Cochran-Lee inequalities. First, we state and prove Levin-Cochran-Lee type inequalities o…
Parabolic equations with concave non-linearity
Zhirayr Avetisyan, Khachatur Khachatryan, Michael Ruzhansky
In this paper we prove the existence and uniqueness of positive mild solutions for the semilinear parabolic equations of the form , where is a p…
Fractional Hardy type inequalities on homogeneous Lie groups in the case
Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan
In this paper, we obtain a fractional Hardy inequality in the case on homogeneous Lie groups, and as an application we show the corresponding uncertainty principle. Also, we…
Evolutionary integro-differential equations of scalar type on locally compact groups
Santiago Gómez Cobos, Joel E. Restrepo, Michael Ruzhansky
We study existence, uniqueness, norm estimates and asymptotic time behaviour (in some cases can be claimed to be sharp) for the solution of a general evolutionary integral (differe…
Global well-posedness of space-time fractional diffusion equation with Rockland operator on graded Lie group
Aparajita Dasgupta, Michael Ruzhansky, Abhilash Tushir
In this article, we examine the general space-time fractional diffusion equation for left-invariant hypoelliptic homogeneous operators on graded Lie groups. Our study covers import…
Lieb-Thirring inequalities on the spheres and
André Pedroso Kowacs, Michael Ruzhansky
In this paper, we obtain new upper bounds for the Lieb-Thirring inequality on the spheres of any dimension greater than . As far as we have checked, our results improve previous…
estimates for non-local heat and wave type equations on locally compact groups
Santiago Gómez Cobos, Joel E. Restrepo, Michael Ruzhansky
We prove the norm estimates for the solutions of heat and wave type equations on a locally compact separable unimodular group by…
Vector Valued Gårding Inequality for pseudo-differential operators on compact homogeneous manifolds
André Kowacs, Michael Ruzhansky
We prove sufficient conditions in order to obtain a sharp Gårding inequality for pseudo-differential operators acting on vector-valued functions on compact Lie groups. As a consequ…
Higher-order evolution inequalities with Hardy potential on the Korányi ball
Mohamed Jleli, Michael Ruzhansky, Bessem Samet +1
We consider a higher order in (time) semilinear evolution inequality posed on the Korányi ball under an inhomogeneous Dirichlet-type boundary condition. The problem involves an inv…
Integro-differential diffusion equations on graded Lie groups
Joel E. Restrepo, Michael Ruzhansky, Berikbol T. Torebek
We first study the existence, uniqueness and well-posedness of a general class of integro-differential diffusion equation on , is a gra…
Time-fractional discrete diffusion equation for Schrödinger operator
Aparajita Dasgupta, Shyam Swarup Mondal, Michael Ruzhansky +1
This article aims to investigate the semi-classical analog of the general Caputo-type diffusion equation with time-dependent diffusion coefficient associated with the discrete Schr…
Semilinear wave inequalities with double damping and potential terms on Riemannian Manifolds
Mohamed Jleli, Michael Ruzhansky, Bessem Samet +1
We study a semilinear wave inequality with double damping on a complete noncompact Riemannian manifold. The considered problem involves a potential function depending on the sp…
Fujita-type results for the degenerate parabolic equations on the Heisenberg groups
Ahmad Z. Fino, Michael Ruzhansky, Berikbol T. Torebek
In this paper, we consider the Cauchy problem for the degenerate parabolic equations on the Heisenberg groups with power law non-linearities. We obtain Fujita-type critical exponen…
Van der Corput lemmas for Mittag-Leffler functions. I
Michael Ruzhansky, Berikbol T. Torebek
In this paper, we study analogues of the van der Corput lemmas involving Mittag-Leffler functions. The generalisation is that we replace the exponential function with the Mittag-Le…