Related papers: Non-formal star-exponential on contracted one-shee…

Sufficient conditions are determined on the parameters such that the generalized and normalized Bessel function of the first kind and other related functions belong to subclasses of starlike and convex functions defined in the unit disk…

We explicitly construct noncommutative * products on circularly symmetric two dimensional space by using the technique of Fedosov's deformation quantization. Especially, on constant curvature spaces i.e., S^2 and H^2, we get su(2) and…

We construct an explicit abelian model for the operation of tensor $2$-product of $2$-representations of $\mathfrak{sl}_{2}^{+}$, specifically the product of a simple $2$-representation $\mathcal{L}(1)$ with a given abelian…

We study the tensor product decomposition of the split real quantum group $U_{q\tilde{q}}(sl(2,R))$ from the perspective of finite dimensional representation theory of compact quantum groups. It is known that the class of positive…

We present a deformed algebra related to the q-exponential and the q-logarithm functions that emerge from nonextensive statistical mechanics. We also develop a q-derivative (and consistently a q-integral) for which the q-exponential is an…

Given a knot K in an integral homology sphere with exterior N_K, there is a natural action of the cyclic group Z/n on the space of SL(n,C) representations of the knot group \pi_1(N_K), and this induces an action on the SL(n,C) character…

Let $A$ be a unital associative algebra over a field $k$. All unital associative algebras containing $A$ as a subalgebra of a given codimension $\mathfrak{c}$ are described and classified. For a fixed vector space $V$ of dimension…

If we add a simple rotation term to both the Ornstein-Uhlenbeck semigroup and the definition of the H-derivative, then analogue to the classical Malliavin calculus on the real Wiener space [I. Shigekawa, Stochastic analysis, 2004], we get a…

We construct a differential algebra of forms on the kappa-deformed space. For a given realization of the noncommutative coordinates as formal power series in the Weyl algebra we find an infinite family of one-forms and nilpotent exterior…

In this report we construct a family of holomorphic functions $\beta_{\lambda,\mu} (s)$ which behave asymptotically like iterated exponentials as $|s| \to \infty$ in the right half plane. Each $\beta_{\lambda,\mu}$ satisfies a convenient…

The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed…

We quantize the Poisson-Lie group SL(2,R)^* as a bialgebra using the product of Kontsevich. The coproduct is a deformation of the coproduct that comes from the group structure. The resulting bialgebra structure is isomorphic to the quantum…

We introduce one- and two-dimensional `exponential shapelets': orthonormal basis functions that efficiently model isolated features in data. They are built from eigenfunctions of the quantum mechanical hydrogen atom, and inherit mathematics…

We give a process to construct non-split, three-dimensional simple Lie algebras from involutions of sl(2,k), where k is a field of characteristic not two. Up to equivalence, non-split three-dimensional simple Lie algebras obtained in this…

We show that irreducible unitary representations of nilpotent super Lie groups can be obtained by induction from a distinguished class of sub super Lie groups. These sub super Lie groups are natural analogues of polarizing subgroups that…

The invariance under unitary representations of the conformal group SL(2,R) of a quantum particle is rigorously investigated in two-dimensional spacetimes containing Killing horizons using DFF model. The limit of the near-horizon…

We develop a generalized Floquet-Bloch theory for discrete torsion-free nilpotent groups by exploiting their Malcev completions. Our main result is a branching formula that relates finite-dimensional representations of a discrete nilpotent…

We investigate the commutativity of global products of functions on the two-sphere from the point of view of a construction started in [RT] and named the skewed product. We complete the construction of the skewed product of functions on the…

In this thesis, we study the structure of the polyhedral product $\mathcal{Z}_{\mathcal{K}}(D^1,S^0)$ determined by an abstract simplicial complex ${\mathcal{K}}$ and the pair $(D^1,S^0)$. We showed that there is natural embedding of the…

Let $ G $ be a connected Lie group with real Lie algebra $ \mathfrak{g}$. Suppose $G$ is also a complex manifold. We obtain explicit holomorphic sectional and bisectional curvature formulas of left-invariant strongly pseudoconvex complex…