Related papers: Integral transform for Logharmonic mappings
We prove the Landau-Ginzburg Mirror Symmetry Conjecture at the level of (orbifolded) Frobenius algebras for a large class of invertible singularities, including arbitrary sums of loops and Fermats with arbitrary symmetry groups.…
This note addresses monotonic growths and logarithmic convexities of the weighted ($(1-t^2)^\alpha dt^2$, $-\infty<\alpha<\infty$, $0<t<1$) integral means $\mathsf{A}_{\alpha,\beta}(f,\cdot)$ and $\mathsf{L}_{\alpha,\beta}(f,\cdot)$ of the…
This paper revisits the classical formulation of the Z-transform and its relationship to the inverse Laplace transform (L-1), originally developed by Ragazzini in sampled-data theory. It identifies a longstanding mathematical oversight in…
The finite Hilbert transform $T$, when acting in the classical Zygmund space $\logl$ (over $(-1,1)$), was intensively studied in \cite{curbera-okada-ricker-log}. In this note an integral representation of $T$ is established via the…
On even-dimensional Euclidean space for integer powers of the Laplace operator greater than or equal to half the dimension, a fundamental solution of the polyharmonic equation has binomial and logarithmic behavior. Gegenbauer polynomial…
We give a class of examples of $A$-hypergeometric systems that display integrality of mirror maps. Specifically, these systems have solutions $F(\lambda_1,\dots,\lambda_N) = 1$ and $\log\lambda^l + G(\lambda_1,\dots,\lambda_N)$ (for certain…
Complexifying space time has many interesting applications, from the construction of higher dimensional unification, to provide a useful framework for quantum gravity and to better define some local symmetries that suffer singularities in…
This mostly expository article explores recent developments in the relations between the three objects in the title from an algebro-combinatorial perspective. We prove a formula for Whittaker functions of a real semisimple group as an…
In this paper we extend the Zeta function regularization technique, which gives a meaningful solution to divergent power series, in order to assign finite values to divergent integral of certain transcendental functions $f(x)$. The…
A series of conjectures is obtained as further investigation of the integral transformation I(alpha) introduced in the previous paper. A Macdonald-type difference operator D is introduced. It is conjectured that D and I(alpha) are…
We generalise Dwork's theory of $p$-adic formal congruences from the univariate to a multi-variate setting. We apply our results to prove integrality assertions on the Taylor coefficients of (multi-variable) mirror maps. More precisely,…
For $\alpha > -1$ and $\beta >0, $ let $\mathcal{B}_{\mathcal{H}}^0(\alpha, \beta)$ denote the class of sense preserving harmonic mappings $f=h+\overline{g}$ in the open unit disk $\mathbb{D}$ satisfying $|zh''(z)+\alpha(h'(z)-1)|\leq…
This paper treats the class of normalized logharmonic mappings f(z) = zh(z)bar{g(z)} in the unit disk satisfying {\phi}(z) = zh(z)g(z) is analytically typically real. Every such mapping f is shown to be a product of two particular…
It turns out that complex geodesics in Teichm\"uller spaces with respect to their invariant metrics are intrinsically connected with variational calculus for univalent functions. We describe this connection and show how geometric features…
A new concept of meromorphic $\Sigma$-factorization, for H\"{o}lder continuous functions defined on a contour $\Gamma$ that is the pullback of $\dot{\mathbb{R}}$ (or the unit circle) in a Riemann surface $\Sigma$ of genus 1, is introduced…
In the study of holomorphic functions of one complex variable, one well-known theory is that of elliptic functions and it is possible to take the zeta-function of Weierstrass as a building stone of this vast theory. We are working the…
An invertible polynomial in $n$ variables is a quasihomogeneous polynomial consisting of $n$ monomials so that the weights of the variables and the quasi-degree are well defined. In the framework of the construction of mirror symmetric…
The article deals with the class ${\mathcal F}_{\alpha }$ consisting of non-vanishing functions $f$ that are analytic and univalent in $\ID$ such that the complement $\IC\backslash f(\ID) $ is a convex set, $f(1)=\infty ,$ $f(0)=1$ and the…
A generalized modular relation of the form $F(z, w, \alpha)=F(z, iw,\beta)$, where $\alpha\beta=1$ and $i=\sqrt{-1}$, is obtained in the course of evaluating an integral involving the Riemann $\Xi$-function. It is a two-variable…
Let $F$ be a non-Archimedean local field of characteristic not equal to 2, let $E/F$ be a finite unramified extension field, and let $\sigma$ be a generator of $\text{Gal}(E, F )$. Let $f$ be an element of $Z(H_{I_E})$, the center of the…