On some extension of Paley Wiener theorem
Concrete Operators, 2020 Paley Wiener theorem characterizes the class of functions which are Fourier transforms of ℂ∞ functions of compact support on ℝn by relating decay properties of those functions or distributions at infinity with analyticity of their Fourier transform.
N’Da Ettien Yves-Fernand, Kangni Kinvi
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The theory of Hahn-meromorphic functions, a holomorphic Fredholm theorem, and its applications [PDF]
, 2012 We introduce a class of functions near zero on the logarithmic cover of the complex plane that have convergent expansions into generalized power series. The construction covers cases where non-integer powers of $z$ and also terms containing $\log z$ can ...
J. Muller, A. Strohmaier
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The Spectra of Banach Algebras of Holomorphic Functions on Polydisk-Type Domains [PDF]
Journal of Geometric Analysis, 2022 Aron et al. (Math Ann 353:293–303, 2012) proved that the Cluster Value Theorem in the infinite dimensional Banach space setting holds for the Banach algebra $$\mathcal {H}^\infty (B_{c_0})$$ H ∞ ( B c 0 ) .
Yunsung Choi, Mingu Jung, M. Maestre
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Variations on Hartogs and Henkin-Tumanov Theorems [PDF]
, 2007 There are equivalent characterizations for holomorphic functions defined on open sets of $\mathbb C^n$; first of all, they can be represented locally as sums of convergent power series.
Mascolo, Raffaella
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Analyticity and Nonanalyticity of Solutions of Delay-Differential Equations [PDF]
SIAM Journal on Mathematical Analysis, 2013 We consider the equation $\dot x(t)=f(t,x(t),x(\eta(t)))$ with a variable time shift $\eta(t)$. Both the nonlinearity $f$ and the shift function $\eta$ are given, and are assumed to be analytic (that is, holomorphic) functions of their arguments ...
J. Mallet-Paret, R. Nussbaum
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Analyticity properties and thermal effects for general quantum field theory on de Sitter space-time [PDF]
, 1998 We propose a general framework for quantum field theory on the de Sitter space-time (i.e. for local field theories whose truncated Wightman functions are not required to vanish).
Bros, Jacques +2 more
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An analog of the Cauchy formula for certain Beltrami equations
Учёные записки Казанского университета: Серия Физико-математические науки, 2019 The Beltrami differential equations are intrinsic generalizations of the Cauchy–Riemann system in complex analysis. Their solutions generalize holomorphic functions. As known, solutions to many problems of the complex analysis are based on application of
D.B. Katz, B.A. Kats
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Quantization scheme for modular q-difference equations [PDF]
, 2004 Modular pairs of some second order q-difference equations are considered. These equations may be interpreted as a quantum mechanics of a sort of hyperelliptic pendulum.
Sergeev, S.
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Two-point Functions and Quantum Fields in de Sitter Universe [PDF]
, 1995 We present a theory of general two-point functions and of generalized free fields in d-dimensional de Sitter space-time which closely parallels the corresponding minkowskian theory.
Bros, J., Moschella, U.
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Vector-valued modular functions for the modular group and the hypergeometric equation [PDF]
, 2007 A general theory of vector-valued modular functions, holomorphic in the upper half-plane, is presented for finite dimensional representations of the modular group.
P. Bantay, T. Gannon
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