6 citations · 14 across the 21 of their papers we have counts for
25 papers
A short note on the dimension of the CC-geodesic Kakeya sets in the first Heisenberg group
Marianna Chatzakou
We study CC-geodesic Kakeya sets in the first Heisenberg group, namely Borel sets such that, for every unit-speed CC-geodesic segment of length issuing from the identity, s…
Fujita exponent for heat equation with Hörmander vector fields
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this paper, we show global existence and non-existence results for the heat equation with some of the squares of smooth vector fields on $\Rn$ satisfying Hörmander's rank condit…
Zero modes and Dirac-(logarithmic) Sobolev-type inequalities
Marianna Chatzakou, Uwe Kahler, Michael Ruzhansky
We study the decay rate of the zero modes of the Dirac operator with a matrix-valued potential that is considered here without any regularity assumptions, compared to the existing…
Nearness and solvability of non-invariant equations on stratified groups
Marianna Chatzakou, Michael Ruzhansky, Nikos Yannakakis
We prove the well-posedness of the differential equation in the setting of a stratified group when the considered second-order differential operator can be…
On global solutions of heat equations with time-dependent nonlinearities on unimodular Lie groups
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this work, we study the global well-posedeness of the heat equation with variable time-dependent nonlinearity of the form on unimodular Lie groups when the differenti…
Sharp upper bound for anisotropic Rényi entropy and Heisenberg uncertainty principle
Marianna Chatzakou, Michael Ruzhansky, Anjali Shriwastawa
In this paper, we prove the anisotropic Shannon inequality for the Renyi entropy with the best constant on Folland-Stein homogeneous Lie groups. As a consequence, we also prove the…
Anharmonic semigroups and applications to global well-posedness of nonlinear heat equations
Duván Cardona, Marianna Chatzakou, Julio Delgado +2
In this work we consider the semigroup for associated to an anharmonic oscillator of the form …
LSTM-CNN: An efficient diagnostic network for Parkinson's disease utilizing dynamic handwriting analysis
Xuechao Wang, Junqing Huang, Sven Nomm +4
Background and objectives: Dynamic handwriting analysis, due to its non-invasive and readily accessible nature, has recently emerged as a vital adjunctive method for the early diag…
Logarithmic Sobolev, Hardy and Poincaré inequalities on the Heisenberg group
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this paper we first prove a number of important inequalities with explicit constants in the setting of the Heisenberg group. This includes the fractional and integer Sobolev, Ga…
Comparison of One- Two- and Three- Dimensional CNN models for Drawing-Test-Based Diagnostics of the Parkinson's Disease
Xuechao Wang, Junqing Huang, Marianna Chatzakou +6
Subject: In this article, convolutional networks of one, two, and three dimensions are compared with respect to their ability to distinguish between the drawing tests produced by P…
Semi-classical pseudo-differential operators on and applications
Linda N. A. Botchway, Marianna Chatzakou, Michael Ruzhansky
In this paper we consider the semiclassical version of pseudo-differential operators on the lattice space . The current work is an extension of a previous work…
Discrete Heat Equation with irregular thermal conductivity and tempered distributional data
Marianna Chatzakou, Aparajita Dasgupta, Michael Ruzhansky +1
In this paper, we consider a semi-classical version of the nonhomogeneous heat equation with singular time-dependent coefficients on the lattice . We establish…
Revised logarithmic Sobolev inequalities of fractional order
Marianna Chatzakou, Michael Ruzhansky
In this short note we prove the logarithmic Sobolev inequality with derivatives of fractional order on with an explicit expression for the constant. Namely, we show…
Degenerate Schrödinger equations with irregular potentials
Duván Cardona, Marianna Chatzakou, Julio Delgado +1
In this work we investigate a class of degenerate Schrödinger equations associated to degenerate elliptic operators with irregular potentials on $\Ran$ by introducing a suitable Hö…
A Light-weight CNN Model for Efficient Parkinson's Disease Diagnostics
Xuechao Wang, Junqing Huang, Marianna Chatzakou +5
In recent years, deep learning methods have achieved great success in various fields due to their strong performance in practical applications. In this paper, we present a light-we…
Heat and wave type equations with non-local operators, II. Hilbert spaces and graded Lie groups
Marianna Chatzakou, Joel E. Restrepo, Michael Ruzhansky
We study heat and wave type equations on a separable Hilbert space by considering non-local operators in time with any positive densely defined linear operator with d…
Schatten-von Neumann properties for Hörmander classes on compact Lie groups
Duván Cardona, Marianna Chatzakou, Michael Ruzhansky +1
Let be a compact Lie group of dimension In this work we characterise the membership of classical pseudo-differential operators on in the trace class ideal $S_{1}(L^2(G…
On a class of anharmonic oscillators II. General case
Marianna Chatzakou, Julio Delgado, Michael Ruzhansky
In this work we study a class of anharmonic oscillators on corresponding to Hamiltonians of the form , where and are functions…
The heat equation with singular potentials. II: Hypoelliptic case
Marianna Chatzakou, Michael Ruzhansky, Niyaz Tokmagambetov
In this paper we consider the heat equation with a strongly singular potential and show that it has a very weak solution. Our analysis is devoted to general hypoelliptic operators…
- Boundedness of Spectral Multipliers of the Anharmonic Oscillator
Marianna Chatzakou, Vishvesh Kumar
In this note we study the boundedness of Fourier multipliers of anharmonic oscillators, and as a consequence also of spectral multipliers, for the range $1<p \leq 2 \leq…
Logarithmic Hardy-Rellich inequalities on Lie groups
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this paper we obtain logarithmic Hardy and Rellich inequalities on general Lie groups. In the case of graded groups, we also show their refinements using the homogeneous Sobolev…
Logarithmic Sobolev-type inequalities on Lie groups
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this paper we show a number of logarithmic inequalities on several classes of Lie groups: log-Sobolev inequalities on general Lie groups, log-Sobolev (weighted and unweighted),…
Anisotropic Shannon inequality
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this note we prove the anisotropic version of the Shannon inequality. This can be conveniently realised in the setting of Folland and Stein's homogeneous groups. We give two pro…
boundedness of Fourier multipliers associated with the anharmonic Oscillator
M. Chatzakou, V. Kumar
In this paper we study the - boundedness of the Fourier multipliers in the setting where the underlying Fourier analysis is introduced with respect to the eigenfunctions…