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Register a new userApproximation of Complex Functions from Weighted Lebesgue space on Carlson Curves
تقريب الدوال العقدية من فضاء ليبيغ الموزن (L_p (Γ,V على منحنيات كارلسون
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Tishreen University ورقة بحثية
Publication date
2015
fields
Mathematics
and research's language is
العربية
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Shamra Editor
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درسنا في هذا البحث مسألة تقريب الدوال العقدية من فضاء ليبيغ الموزن و (وزن ماكنهوبت)، إلى دوال كسرية متعلقة بكثيرات حدود p – فابير و ذلك على أسرة واسعة من المنحنيات تدعى منحنيات كارلسون، كما و يعد هذا العمل بمثابة متابعة لما قام به الباحثان Israfilov و Testici عام 2014 ، حيث درسا تقريب الدوال العقدية من فضاء سميرنوف الموزن على مناطق محاطة بمنحنيات كارلسون.
In this research, we have studied the issue of approximation of complex functions from weighted Lebesgue space ; and (Mukenhoupt weight) to rational functions by using p- Faber polynomials on large group of curves, which called Carlson curves. This is also considered as a follow-up to the work done by researchers: Israfilov and Testici in 2014 , where they studied approximation of functions from weighted Smirnov space on domains with a Carlson curve boundary.
References used
BÖTTCHER.A; KARLOVICH.A.Y. Carleson Curves, Muckenhoupt Weights, and Toeplitz Operators. Springer Basel AG, Washington D.C, 1997, 407
DAVID.G. Operateurs integraux singulers sur certaines courbes du plan complexe. Vol 17 (4), Ann. Sci. Ecole Norm. Sup, 1984, 157-189
ISRAFILOV. D.M. Approximation by p-faber polynomials in the weighted smirnov class , P E G W and Bieberbach Polynomials. Vol 17, Constr. Approx. 2001, 335- 351
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We study in this research approximation of complex functions from Orlicz space on a subclass of Carlson curves, which called Dini smooth curves to rational functions by using polynomials related with Dzjadyk sums which obtained from Faber polynomials. We depend on some concepts of complex analysis such as formulas of Sokhotski to reach the desired goal
In this work, we have studied the issue of approximation of functions from Morrey
space ; by rational functions on a large group of curves,
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Smirnov space defined on a finite domain with a boundary belonging to Dini- smooth
curves by polynomials is obtained.
We study in this paper one of functional analysis problems, involved with
construction a new class of functions, denoted by . The definition of the new
class depends on definition of Lebesgueclass of functions and on the Holder clas .
We study the
relation between the new class and approximation of the new class
to rational functions.
This research aimed to define a new class of complex functions , which depends in its definition on the definition of famous Holder class. We studied the relation between the new and Holder classes, then we proved some properties of the class.
We fi
nally applied this study to approximate the class of complex functions on closed curves , which belong to a wide class of curves.
The aim of this research is to present the two new classes of complex functions . The first class is denoted , and the second one is denoted. The definition of both of them depends on the famous Lebesgue class ,and orlicz class .The relationship bet
ween the two new classes the two classes is studied. This study gives some properties .
Finally, this study is used for approximation of the class on group of wide curves.
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