A continuous function f on the torus exists with hat f(2^k)=a_k and hat f zero outside the unions of intervals [2^k-r_k,2^k+r_k] for every a satisfying sum |a_k|^2 w_k^2 finite if and only if the supremum over k of the partial sums of w_n^{-2} from log2(r_k) to k remains finite.
Title resolution pending
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.CA 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Fourier coefficients of continuous functions with sparse spectrum
A continuous function f on the torus exists with hat f(2^k)=a_k and hat f zero outside the unions of intervals [2^k-r_k,2^k+r_k] for every a satisfying sum |a_k|^2 w_k^2 finite if and only if the supremum over k of the partial sums of w_n^{-2} from log2(r_k) to k remains finite.