Related papers: Harmonic Univalent Functions Defined by Post Quant…
In this paper we have introduced two new classes $\mathcal{H}\mathcal{M}(\beta, \lambda, k, \nu)$ and $\overline{\mathcal{H}\mathcal{M}} (\beta, \lambda, k, \nu)$ of complex valued harmonic multivalent functions of the form $f = h +…
In this study, we derive the sharp bounds of certain Toeplitz determinants whose entries are the coefficients of holomorphic functions belonging to a class defined on the unit disk $\mathbb{U}$. Further, these results are extended to a…
Let $Co(\alpha)$ denote the class of concave univalent functions in the unit disk $\ID$. Each function $f\in Co(\alpha)$ maps the unit disk $\ID$ onto the complement of an unbounded convex set. In this paper we find the exact disk of…
The decompositions of an element of a finite von Neumann algebra into the sum of a normal operator plus an s.o.t.-quasinilpotent operator, obtained using the Haagerup--Schultz hyperinvariant projections, behave well with respect to…
It is proved that harmonic functions are characterized by harmonicity of their spherical means, for which purpose the iterated spherical means are used. The similar characterization of solutions to the modified Helmholtz equation…
For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…
A holomorphic family of closed operators with a rank one perturbation given by the function $x^{\frac{m}{2}}$ is studied. The operators can be used in a toy model of renormalization group.
We define a one-parameter family of two-sided coideals in U_q(gl(n)) and study the corresponding algebras of infinitesimally right invariant functions on the quantum unitary group U_q(n). The Plancherel decomposition of these algebras with…
We study three functions which are power series in the variable $z$, Dirichlet series in the variable $s$ and with coefficients given by arithmetical functions. A strong point is to relate these functions to some Hilbert spaces. Three main…
Partition functions of certain classes of "spin glass" models in statistical physics show strong connections to combinatorial graph invariants. Also known as homomorphism functions they allow for the representation of many such invariants,…
In this paper we characterize some basic properties of composition operators on the spaces of harmonic Bloch functions. First we provide some equivalent conditions for boundedness and compactness of composition operators. Then by using…
We consider an infinite family of non-rational conformal field theories in the presence of a conformal boundary. These theories, which have been recently proposed in arXiv:0803.2099, are parameterized by two real numbers (b,m) in such a way…
Concrete sharp constants in a pointwise estimate of the gradient of a harmonic function in the unit disk are obtained under the assumption that function belong to Hardy space $h^p$, $p\ge 1$. This generalizes some recent result of Maz'ya &…
Our previous work (math.QA/9808015) introduces the basic notions and announces some results on function theory in the quantum disc. The present paper establishes a relationship between those results and the quantum groups theory.
It is a classical theorem that if a function is integrable along the boundary of the unit circle, then the function is the nontangential limit of a holomorphic function on the open disc if and only if its Fourier coefficients for…
In the present paper we introduce the notion of harmonicity modulus and harmonicity K-functional and apply these notions to prove a Jackson type theorem for approximation of continuous functions by polyharmonic functions. For corresponding…
The conventional paradigm of quantum computing is discrete: it utilizes discrete sets of gates to realize bitstring-to-bitstring mappings, some of them arguably intractable for classical computers. In parameterized quantum approaches, the…
We use the density function of a harmonic space to obtain estimates for the eigenvalues of the Jacobi operator; when these estimates are sharp, then the harmonic space is a symmetric Osserman space.
In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by…
The concepts of amenable and compatible functions have been introduced in a recent work, in order to state precise mathematical theorems that guarantee that a backward stable algorithm is also forward stable, and that the composition of two…