11 citations · 54 across the 23 of their papers we have counts for
26 papers
Very weak solutions of the heat equation with anisotropically singular time-dependent diffusivity
Zhirayr Avetisyan, Zahra Keyshams, Monire Mikaeili Nia +1
We investigate the heat equation with a time-dependent, anisotropic, and potentially singular diffusivity tensor. Since weak (in the Sobolev sense) or distributional solutions may…
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…
Very weak solutions of the heat equation with anisotropically singular time-dependent diffusivity
Zhirayr Avetisyan, Zahra Keyshams, Monire Mikaeili Nia +1
We investigate the heat equation with a time-dependent, anisotropic, and potentially singular diffusivity tensor. Since weak (in the Sobolev sense) or distributional solutions may…
On a unique two-dimensional integral operator homogeneous with respect to all orientation preserving linear transformations
Zhirayr Avetisyan, Alexey Karapetyants, Adolf Mirotin
In this paper, we consider a two-dimensional operator with an antisymmetric integral kernel, recently introduced by Z. Avetisyan and A. Karapetyants in connection to the study of g…
Exponential decay estimates for the resolvent kernel on a Riemannian manifold
Zhirayr Avetisyan
On a complete, connected, non-compact Riemannian manifold, with Ricci curvature bounded from below, we establish exponential decay estimates at infinity for the spherical sums of t…
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…
Mixed Fourier norm spaces of analytic functions on the upper half-plane and Toeplitz operators
Zhirayr Avetisyan, Alexey Karapetyants, Irina Smirnova
We introduce and study weighted spaces of functions with mixed norm on the upper half-plane, defined in terms of Fourier transform. We give a characterization of analytic functions…
Mixed-Fourier-norm spaces and holomorphic functions
Zhirayr Avetisyan, Alexey Karapetyants
We describe a general framework of functional and Fourier analysis on domains with a free action of an Abelian Lie group . Namely, on a domain of the form we introdu…
A note on the polar decomposition in metric spaces
Zhirayr Avetisyan, Michael Ruzhansky
The analogue of polar coordinates in the Euclidean space, a polar decomposition in a metric space, if well-defined, can be very useful in dealing with integrals with respect to a s…
Invariant Geometric Structures on Almost Abelian Lie Groups
Zhirayr Avetisyan, Abigail Brauer, Oderico-Benjamin Buran +2
An almost Abelian group is a non-Abelian Lie group with a codimension 1 Abelian subgroup. This paper investigates invariant Hermitian and Kähler structures on connected complex alm…
Topological Properties of Almost Abelian Groups
Zhirayr Avetisyan, Oderico-Benjamin Buran, Andrew Paul +1
An almost Abelian Lie group is a non-Abelian Lie group with a codimension 1 Abelian subgroup. We show that all discrete subgroups of complex simply connected almost Abelian groups…
Elements (functions) that are universal with respect to a minimal system
Zhirayr Avetisyan, Martin Grigoryan, Michael Ruzhansky
We call an element conditionally universal for a sequential convergence space with respect to a minimal system in a continuously and densely e…
Nonlinear (chiral) p-form electrodynamics
Zhirayr Avetisyan, Oleg Evnin, Karapet Mkrtchyan
In our previous article Phys. Rev. Lett. 127 (2021) 271601, we announced a novel 'democratic' Lagrangian formulation of general nonlinear electrodynamics in four dimensions that fe…
Homogeneous operators and homogeneous integral operators
Zhirayr Avetisyan, Alexey Karapetyants
We introduce and study in a general setting the concept of homogeneity of an operator and, in particular, the notion of homogeneity of an integral operator. In the latter case, hom…
Democratic Lagrangians for Nonlinear Electrodynamics
Zhirayr Avetisyan, Oleg Evnin, Karapet Mkrtchyan
We construct a Lagrangian for general nonlinear electrodynamics that features electric and magnetic potentials on equal footing. In the language of this Lagrangian, discrete and co…
Rigidity of a thin domain depends on the curvature, width, and boundary conditions
Zhirayr Avetisyan, Davit Harutyunyan, Narek Hovsepyan
This paper is concerned with the study of linear geometric rigidity of shallow thin domains under zero Dirichlet boundary conditions on the displacement field on the thin edge of t…
Almost Abelian Lie groups, subgroups and quotients
Marcelo Almora Rios, Zhirayr Avetisyan, Katalin Berlow +5
An almost Abelian Lie group is a non-Abelian Lie group with a codimension 1 Abelian normal subgroup. The majority of 3-dimensional real Lie groups are almost Abelian, and they appe…
Global hyperbolicity and factorization in cosmological models
Zhirayr Avetisyan
The subject of the paper is the geometry and topology of cosmological spacetimes and vector bundles thereon, which are used to model physical fields propagating in the universe. Gl…
Jordanable almost Abelian Lie algebras
Zhirayr Avetisyan
We call a linear operator on a vector space over a field Jordanable if it has a Jordan canonical form. An almost Abelian Lie algebra has only one non-vanishing Lie bracket, which i…
Approximations in with convergent Fourier series
Zhirayr Avetisyan, Martin Grigoryan, Michael Ruzhansky
For a separable finite diffuse measure space and an orthonormal basis of consisting of bounded functions ,…
The second Weyl coefficient for a first order system
Zhirayr Avetisyan, Johannes Sjoestrand, Dmitri Vassiliev
For a scalar elliptic self-adjoint operator on a compact manifold without boundary we have two-term asymptotics for the number of eigenvalues between zero and lambda when lambda te…
Analytic definition of spin structure
Zhirayr Avetisyan, Yan-Long Fang, Nikolai Saveliev +1
We work on a parallelizable time-orientable Lorentzian 4-manifold and prove that in this case the notion of spin structure can be equivalently defined in a purely analytic fashion.…
The structure of almost Abelian Lie algebras
Zhirayr Avetisyan
An almost Abelian Lie algebra is a non-Abelian Lie algebra with a codimension 1 Abelian ideal. Most 3-dimensional real Lie algebras are almost Abelian, and they appear in every bra…
Spectral asymptotics for first order systems
Zhirayr Avetisyan, Yan-Long Fang, Dmitri Vassiliev
This is a review paper outlining recent progress in the spectral analysis of first order systems. We work on a closed manifold and study an elliptic self-adjoint first order system…