scholarly journals Real-Analytic Non-Integrable Functions on the Plane with Equal Iterated Integrals

2021 ◽  
Vol 77 (1) ◽  
Author(s):  
Luis Bernal-González ◽  
María del Carmen Calderón-Moreno ◽  
Andreas Jung
Keyword(s):  
Vector Space ◽  
Analytic Functions ◽  
Continuous Functions ◽  
Compact Open Topology ◽  
Real Numbers ◽  
Iterated Integrals ◽  
Integrable Functions ◽  
Real Analytic Functions ◽  
Real Analytic

AbstractIn this note, a vector space of real-analytic functions on the plane is explicitly constructed such that all its nonzero functions are non-integrable but yet their two iterated integrals exist as real numbers and coincide. Moreover, it is shown that this vector space is dense in the space of all real continuous functions on the plane endowed with the compact-open topology.

scholarly journals The Lagrangian Stability for a Class of Second-Order Quasi-Periodic Reversible Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Yanling Shi ◽  
Jia Li
Keyword(s):  
Differential Equation ◽  
Analytic Functions ◽  
Order Differential Equation ◽  
Reversible Systems ◽  
Invariant Curves ◽  
Real Analytic Functions ◽  
All Solutions ◽  
Small Twist Theorem ◽  
Real Analytic ◽  
Twist Theorem

We study the following two-order differential equation,(Φp(x'))'+f(x,t)Φp(x')+g(x,t)=0,whereΦp(s)=|s|(p-2)s,p>0.f(x,t)andg(x,t)are real analytic functions inxandt,2aπp-periodic inx, and quasi-periodic intwith frequencies(ω1,…,ωm). Under some odd-even property off(x,t)andg(x,t), we obtain the existence of invariant curves for the above equations by a variant of small twist theorem. Then all solutions for the above equations are bounded in the sense ofsupt∈R|x′(t)|<+∞.

On zero sets of harmonic and real analytic functions

2018 ◽  
Vol 42 (2) ◽  
pp. 159-167
Author(s):  
André Boivin ◽  
Paul M. Gauthier ◽  
Myrto Manolaki
Keyword(s):  
Analytic Functions ◽  
Zero Sets ◽  
Real Analytic Functions ◽  
Real Analytic

scholarly journals On the Construction of Large Algebras Not Contained in the Image of the Borel Map

2019 ◽  
Vol 75 (1) ◽  
Author(s):  
Céline Esser ◽  
Gerhard Schindl
Keyword(s):  
Sequence Space ◽  
Analytic Functions ◽  
General Setting ◽  
Smooth Functions ◽  
The Real ◽  
Cauchy Product ◽  
Real Analytic Functions ◽  
Borel Map ◽  
Real Analytic ◽  
The Stability

AbstractThe Borel map $$j^{\infty }$$j∞ takes germs at 0 of smooth functions to the sequence of iterated partial derivatives at 0. It is well known that the restriction of $$j^{\infty }$$j∞ to the germs of quasianalytic ultradifferentiable classes which are strictly containing the real analytic functions can never be onto the corresponding sequence space. In a recent paper the authors have studied the size of the image of $$j^{\infty }$$j∞ by using different approaches and worked in the general setting of quasianalytic ultradifferentiable classes defined by weight matrices. The aim of this paper is to show that the image of $$j^{\infty }$$j∞ is also small with respect to the notion of algebrability and we treat both the Cauchy product (convolution) and the pointwise product. In particular, a deep study of the stability of the considered spaces under the pointwise product is developed.

scholarly journals Limits of quotients of bivariate real analytic functions

2013 ◽  
Vol 50 ◽  
pp. 197-207 ◽  
Author(s):  
C. Cadavid ◽  
S. Molina ◽  
J.D. Vélez
Keyword(s):  
Analytic Functions ◽  
Real Analytic Functions ◽  
Real Analytic
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