A quantitative version of the Beurling-Helson theorem
نویسندگان
چکیده
منابع مشابه
Quantitative aspects of the Beurling–Helson theorem: Phase functions of a special form
We consider the space A(T), d ≥ 2, of absolutely convergent Fourier series on the torus T. The norm on A(T) is naturally defined by ‖f‖A = ‖f̂‖l1 , where f̂ is the Fourier transform of a function f . For phase functions φ of a certain special form, we obtain lower bounds for the A -norms of the exponentials e as λ → ∞. In particular, we show that if φ(x, y) = a(x)|y| for |y| ≤ π, where a ∈ A(T) i...
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ژورنال
عنوان ژورنال: Functional Analysis and Its Applications
سال: 2015
ISSN: 0016-2663,1573-8485
DOI: 10.1007/s10688-015-0093-0