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Bounds on Hankel Determinants with Fekete-Szegö Parameter for Bazilević Functions [version 2; peer review: 2 approved, 1 not approved] [PDF]
F1000ResearchBackground In Geometric Function Theory, a central area of complex analysis, researchers study the geometric properties of analytic and univalent functions in the unit disk.
Abdul Rahman S.Juma, Nathir Khaled
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Koopman–von Neumann and Weyl–Wigner Phase-Space Formulation of Inviscid Euler Flows [PDF]
EntropyWe develop a unified Koopman–von Neumann (KvN) operator and Weyl–Wigner phase-space framework for inviscid ideal (barotropic) Euler flows. Our approach reformulates the nonlinear fluid dynamics as a linear KvN evolution on an enlarged field phase space ...
Sandor M. Molnar, Joseph R. Godfrey
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Crossing antisymmetric Polyakov blocks + dispersion relation
Journal of High Energy Physics, 2022 Many CFT problems, e.g. ones with global symmetries, have correlation functions with a crossing antisymmetric sector. We show that such a crossing antisymmetric function can be expanded in terms of manifestly crossing antisymmetric objects, which we call
Apratim Kaviraj
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Normality of Composite Analytic Functions and Sharing an Analytic Function [PDF]
Fixed Point Theory and Applications, 2010 AbstractA result of Hinchliffe (2003) is extended to transcendental entire function, and an alternative proof is given in this paper. Our main result is as follows: let "Equation missing" be an analytic function, "Equation missing" a family of analytic functions in a domain "Equation missing", and "Equation missing" a transcendental entire function. If
Qifeng Wu, Bing Xiao, Wenjun Yuan
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q-analytic functions, fractals and generalized analytic functions [PDF]
Journal of Physics A: Mathematical and Theoretical, 2014 We introduce a new class of complex functions of complex argument which we call q-analytic functions. These functions satisfy q-Cauchy–Riemann equations and have real and imaginary parts as q-harmonic functions. We show that q-analytic functions are not the analytic functions.
Pashaev, Oktay K., Nalci, Sengul
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Charging up the functional bootstrap
Journal of High Energy Physics, 2021 We revisit the problem of bootstrapping CFT correlators of charged fields. After discussing in detail how bounds for uncharged fields can be recycled to the charged case, we introduce two sets of analytic functional bases for correlators on the line. The
Kausik Ghosh +2 more
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A basis of analytic functionals for CFTs in general dimension
Journal of High Energy Physics, 2021 We develop an analytic approach to the four-point crossing equation in CFT, for general spacetime dimension. In a unitary CFT, the crossing equation (for, say, the s- and t-channel expansions) can be thought of as a vector equation in an infinite ...
Dalimil Mazáč +2 more
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An Analytic Characterization of p,q-White Noise Functionals
Journal of Mathematics, 2020 In this paper, a characterization theorem for the S-transform of infinite dimensional distributions of noncommutative white noise corresponding to the p,q-deformed quantum oscillator algebra is investigated.
Anis Riahi +3 more
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Analytic functional bootstrap for CFTs in d > 1
Journal of High Energy Physics, 2020 We introduce analytic functionals which act on the crossing equation for CFTs in arbitrary spacetime dimension. The functionals fully probe the constraints of crossing symmetry on the first sheet, and are in particular sensitive to the OPE, (double ...
Miguel F. Paulos
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Archive for Mathematical Logic, 2016 We introduce the notion of $R$-analytic functions. These are definable in an o-minimal expansion of a real closed field $R$ and are locally the restriction of a $K$-differentiable function (defined by Peterzil and Starchenko) where $K=R[\sqrt{-1}]$ is the algebraic closure of $R$.
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