کد مقاله کد نشریه سال انتشار مقاله انگلیسی ترجمه فارسی نسخه تمام متن
4661603 1344847 2016 18 صفحه PDF ندارد دانلود رایگان
عنوان انگلیسی مقاله
Undecidability through Fourier series
ترجمه فارسی عنوان
تصمیم ناپذیری از طریق از سری‌های فوریه
کلمات کلیدی
مجموعه بازگشتی قابل شمارش؛ سری‌های فوریه؛ مسئله BUCHI . توابع تتا ژاکوبی
03D25; 42B05; 11Y55; 33E05Recursively enumerable sets; Fourier series; Büchi's problem; Jacobi theta functions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی

In computability theory a variety of combinatorial systems are encountered (word problems, production systems) that exhibit undecidability properties. Here we seek such structures in the realm of Analysis, more specifically in the area of Fourier Analysis. The starting point is that sufficiently strongly convergent Fourier series give rise to predicates in the sense of first order predicate calculus by associating to any s  -ary Fourier series the predicate “the Fourier coefficient with index (n1,…,ns)(n1,…,ns) is non-zero”. We introduce production systems, viewed as counterparts of the combinatorial ones, that generate all recursively enumerable predicates in this way using as tools only elementary operations and functions from classical Analysis. The problem arises how simple such a system may be. It turns out that there is a connection between this question and an as yet unproved conjecture by R. Büchi. This is discussed in the second half of the paper.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 167, Issue 7, July 2016, Pages 507–524
نویسندگان
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