scholarly journals An example of a real analytic strongly pseudoconvex hypersurface which is not holomorphically equivalent to any algebraic hypersurface

2001 ◽  
Vol 39 (1) ◽  
pp. 75-93 ◽  
Author(s):  
Xiaojun Huang ◽  
Shanyu Ji ◽  
Stephen S. T. Yau
Keyword(s):  
Algebraic Hypersurface ◽  
Real Analytic ◽  
Pseudoconvex Hypersurface

The Moments of Real Analytic Funtions

2020 ◽  
pp. 112-118 ◽  
Author(s):  
Ricardo Estrada
Keyword(s):  
Real Analytic

On finite sums of periodic functions

2020 ◽  
Vol 27 (2) ◽  
pp. 265-269
Author(s):  
Alexander Kharazishvili
Keyword(s):  
Analytic Function ◽  
Real Line ◽  
Real Analytic Function ◽  
Periodic Functions ◽  
Uniform Limit ◽  
The Real ◽  
Pointwise Limit ◽  
Finite Sums ◽  
Real Analytic

AbstractIt is shown that any function acting from the real line {\mathbb{R}} into itself can be expressed as a pointwise limit of finite sums of periodic functions. At the same time, the real analytic function {x\rightarrow\exp(x^{2})} cannot be represented as a uniform limit of finite sums of periodic functions and, simultaneously, this function is a locally uniform limit of finite sums of periodic functions. The latter fact needs the techniques of Hamel bases.

scholarly journals Modular invariance in finite temperature Casimir effect

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Francesco Alessio ◽  
Glenn Barnich
Keyword(s):  
Partition Function ◽  
Chemical Potential ◽  
Casimir Effect ◽  
Temperature Inversion ◽  
Massless Scalar ◽  
Partition Functions ◽  
Parallel Plates ◽  
Modular Transformations ◽  
Real Analytic ◽  
Set Up

Abstract The temperature inversion symmetry of the partition function of the electromagnetic field in the set-up of the Casimir effect is extended to full modular transformations by turning on a purely imaginary chemical potential for adapted spin angular momentum. The extended partition function is expressed in terms of a real analytic Eisenstein series. These results become transparent after explicitly showing equivalence of the partition functions for Maxwell’s theory between perfectly conducting parallel plates and for a massless scalar with periodic boundary conditions.

scholarly journals Eisenstein series and an asymptotic for the K-Bessel function

2021 ◽  
Author(s):  
Jimmy Tseng
Keyword(s):  
Asymptotic Expansion ◽  
Bessel Function ◽  
Eisenstein Series ◽  
Uniform Estimate ◽  
Positive Real ◽  
Dominant Term ◽  
Complex Order ◽  
Fixed Parameter ◽  
Real Argument ◽  
Real Analytic

AbstractWe produce an estimate for the K-Bessel function $$K_{r + i t}(y)$$ K r + i t ( y ) with positive, real argument y and of large complex order $$r+it$$ r + i t where r is bounded and $$t = y \sin \theta $$ t = y sin θ for a fixed parameter $$0\le \theta \le \pi /2$$ 0 ≤ θ ≤ π / 2 or $$t= y \cosh \mu $$ t = y cosh μ for a fixed parameter $$\mu >0$$ μ > 0 . In particular, we compute the dominant term of the asymptotic expansion of $$K_{r + i t}(y)$$ K r + i t ( y ) as $$y \rightarrow \infty $$ y → ∞ . When t and y are close (or equal), we also give a uniform estimate. As an application of these estimates, we give bounds on the weight-zero (real-analytic) Eisenstein series $$E_0^{(j)}(z, r+it)$$ E 0 ( j ) ( z , r + i t ) for each inequivalent cusp $$\kappa _j$$ κ j when $$1/2 \le r \le 3/2$$ 1 / 2 ≤ r ≤ 3 / 2 .

Inversion of the geomagnetic induction problem

1970 ◽  
Vol 315 (1521) ◽  
pp. 185-194 ◽  
Keyword(s):  
Frequency Spectrum ◽  
Real Data ◽  
Real Analytic Function ◽  
Numerical Application ◽  
Geomagnetic Induction ◽  
Induction Equation ◽  
Real Analytic ◽  
Principle Of Causality ◽  
Magnetic Potentials ◽  
Magnetic Induction Equation

An algorithm has been found for inverting the problem of geomagnetic induction in a con­centrically stratified Earth. It determines the (radial) conductivity distribution from the frequency spectrum of the ratio of internal to external magnetic potentials of any surface harmonic mode. The derivation combines the magnetic induction equation with the principle of causality in the form of an integral constraint on the frequency spectrum. This algorithm generates a single solution for the conductivity. This solution is here proved unique if the conductivity is a bounded, real analytic function with no zeros. Suggestions are made regarding the numerical application of the algorithm to real data.

scholarly journals Real analytic generalized functions

2008 ◽  
Vol 156 (1) ◽  
pp. 85-102 ◽  
Author(s):  
S. Pilipović ◽  
D. Scarpalezos ◽  
V. Valmorin
Keyword(s):  
Generalized Functions ◽  
Real Analytic

scholarly journals On real-analytic recurrence relations for cardinal exponential B-splines

2007 ◽  
Vol 145 (2) ◽  
pp. 253-265 ◽  
Author(s):  
J.M. Aldaz ◽  
O. Kounchev ◽  
H. Render
Keyword(s):  
Recurrence Relations ◽  
B Splines ◽  
Real Analytic

scholarly journals Some properties of Grauert type surfaces

2017 ◽  
Vol 28 (08) ◽  
pp. 1750063 ◽  
Author(s):  
Samuele Mongodi ◽  
Zbigniew Slodkowski ◽  
Giuseppe Tomassini
Keyword(s):  
Convex Space ◽  
Level Sets ◽  
Double Cover ◽  
Classification Theorem ◽  
Stein Space ◽  
Pluriharmonic Function ◽  
Exhaustion Function ◽  
Real Analytic ◽  
Complete Surfaces

In a previous work, we classified weakly complete surfaces which admit a real analytic plurisubharmonic exhaustion function; we showed that, if they are not proper over a Stein space, then they admit a pluriharmonic function, with compact Levi-flat level sets foliated with dense complex leaves. We called these Grauert type surfaces. In this note, we investigate some properties of these surfaces. Namely, we prove that the only compact curves that can be contained in them are negative in the sense of Grauert and that the level sets of the pluriharmonic function are connected, thus completing the analogy with the Cartan–Remmert reduction of a holomorphically convex space. Moreover, in our classification theorem, we had to pass to a double cover to produce the pluriharmonic function; the last part of the present paper is devoted to the construction of an example where passing to a double cover cannot be avoided.

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