Selected Publications
This paper extends classical cosine functional equations to operator-valued functions on locally compact groups, introducing a generalized “Hilbert cosine” framework. It characterizes bounded operator solutions using harmonic analysis and group representation techniques.
Exploration of the structural and topological properties of homogeneous spaces, focusing on a class of properties denoted as (Pp). These properties relate to the behavior of locally compact groups acting transitively on topological spaces, and the implications for amenability, compactness, and invariant measures.
We examine the conditions under which a homogeneous space 𝐺/𝐻 - formed by a locally compact group 𝐺 and a closed subgroup 𝐻 - can be considered amenable. The notion of amenability, originally developed in the context of groups, is extended here to quotient spaces, with emphasis on the existence of invariant means and measures.
We define new classes of generalized spherical distributions and analyze their invariance and transformation properties.
This paper develops a specialized version of the spherical Fourier transform—called the type δ transform—and applies it to the harmonic analysis of semi-simple Lie groups, particularly in the context of their unitary representations and symmetric spaces.
We introduce and analyze the spherical trace Fourier transform, a specialized tool in harmonic analysis designed for functions on semi-simple Lie groups that exhibit spherical symmetry. It extends classical Fourier analysis by incorporating trace operations over compact subgroups, offering new insights into representation theory and the structure of symmetric spaces.
This paper addresses an important structural question in non-associative algebra by extending the classical theory of Cartan subalgebras to the setting of Malcev superalgebras.
The paper introduces and studies generalized spherical distributions on the Heisenberg group, extending classical spherical analysis to this non-commutative setting. It characterizes these distributions through their invariance under group actions and derives corresponding integral representations and convolution properties. The results deepen the understanding of harmonic analysis on nilpotent Lie groups.
The paper defines and analyzes the spherical Fourier transform of type δ, a generalization of the classical spherical Fourier transform on homogeneous spaces. It establishes key properties such as inversion formulas, Plancherel relations, and convolution identities, showing how this δ-type transform extends harmonic analysis techniques to broader classes of functions and distributions.
The paper investigates the cohomology theory of Malcev II algebras, a non-associative generalization of Lie algebras. It constructs corresponding cochain complexes and coboundary operators, establishing fundamental properties of low-dimensional cohomology groups. The results provide insights into deformation theory and representation structures of Malcev-type algebras.
The paper develops a framework for special functions defined on the space of positive definite matrices, extending classical scalar functions to matrix domains. It studies their integral representations, invariance properties, and differential equations, linking them to harmonic analysis on symmetric cones. The results generalize well-known functions such as Bessel and hypergeometric types to matrix settings.
The conference paper provides an introductory overview of the representation theory of compact groups, emphasizing its applications in theoretical and mathematical physics. It outlines fundamental concepts such as unitary representations, characters, and Peter–Weyl decomposition, illustrating how these tools apply to symmetry analysis in gauge and fiber bundle theories.
We examine convolution operators on nilpotent Lie groups, focusing on their boundedness and spectral properties. We establish conditions for their L^p continuity.
The paper explores applications of Reiter’s condition in harmonic analysis on locally compact groups. It demonstrates how Reiter’s framework characterizes amenability and yields criteria for invariant means and fixed-point properties. Several examples illustrate its role in connecting abstract harmonic analysis with representation theory.
This work develops the theory of amenable homogeneous spaces and examines their connection with unitary representations of semi-direct product groups. It characterizes amenability through invariant means and induced representations, providing new criteria for the existence of irreducible components. The results unify aspects of harmonic analysis and representation theory on non-compact groups.
We study structural and analytical properties of amenable homogeneous spaces in the context of locally compact groups. We establish conditions under which such spaces admit invariant means and explores implications for harmonic analysis and representation theory. The results extend known criteria for group amenability to broader homogeneous settings.
We construct a generalization of the Ambarzumian integral equation is a nonlinear integral equation arising from radiative transfer theory in stellar atmospheres, developed by Viktor Ambartsumian in the 1940s for problems involving scattering in semi-infinite atmospheres and reflection functions..
We give a necessary condition for a function to be expressed as the Fourier transform of a probability distribution.
This work addresses a key integral equation in stellar statistics by proposing a new inversion method that ensures existence and uniqueness under appropriate conditions. It derives explicit formulas for recovering spatial stellar densities from observable data. The approach improves upon classical treatments by reducing reliance on restrictive model assumptions.
The paper presents a method for solving the Ambarzumian integral equation, which arises in inverse spectral problems of Sturm–Liouville type. It establishes conditions for existence and uniqueness of solutions and provides explicit reconstruction formulas for the potential function. The results refine and generalize earlier approaches to this classical inverse problem. .