کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6418282 1339325 2014 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Topological genericity of nowhere differentiable functions in the disc and polydisc algebras
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Topological genericity of nowhere differentiable functions in the disc and polydisc algebras
چکیده انگلیسی

In this paper we examine functions in the disc algebra A(D) and the polydisc algebra A(DI), where I is a finite or countably infinite set. We prove that, generically, for every f∈A(D) the continuous periodic functions u=Ref|T and u˜=Imf|T are nowhere differentiable on the unit circle T. Afterwards, we generalize this result by proving that, generically, for every f∈A(DI), where I is as above, the continuous periodic functions u=Ref|TI and u˜=Imf|TI have no directional derivatives at any point of TI and every direction v∈RI with ‖v‖∞=1. Finally, we describe how our proofs can be modified to give similar results for nowhere Hölder functions in these algebras.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 420, Issue 1, 1 December 2014, Pages 435-446
نویسندگان
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