کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5775149 | 1413576 | 2017 | 34 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Finite Blaschke products and the construction of rational Î-inner functions
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
LetÎ=def{(z+w,zw):|z|â¤1,|w|â¤1}âC2. A Î-inner function is a holomorphic map h from the unit disc D to Î whose boundary values at almost all points of the unit circle T belong to the distinguished boundary bÎ of Î. A rational Î-inner function h induces a continuous map h|T from T to bÎ. The latter set is topologically a Möbius band and so has fundamental group Z. The degree of h is defined to be the topological degree of h|T. In a previous paper the authors showed that if h=(s,p) is a rational Î-inner function of degree n then s2â4p has exactly n zeros in the closed unit disc Dâ, counted with an appropriate notion of multiplicity. In this paper, with the aid of a solution of an interpolation problem for finite Blaschke products, we explicitly construct the rational Î-inner functions of degree n with the n zeros of s2â4p prescribed.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 447, Issue 2, 15 March 2017, Pages 1163-1196
Journal: Journal of Mathematical Analysis and Applications - Volume 447, Issue 2, 15 March 2017, Pages 1163-1196
نویسندگان
Jim Agler, Zinaida A. Lykova, N.J. Young,