The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sido...The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sidon series taking values in a Banach space: the summability on a set of positive measure implies the almost everywhere convergence; the contraction principle of Billard-Kahane remains true for Sidon series. As applications, they extend a uniqueness theorem of Zygmund concerning lacunary Fourier series and an analytic continuation theorem of Hadamard concerning lacunary Taylor series. Some of their results still hold for Sidon sets of second kind.展开更多
In this paper,we firstly construct several new kinds of Sidon spaces and Sidon sets by investigating some known results.Secondly,using these Sidon spaces,we will present a construction of cyclic subspace codes with ca...In this paper,we firstly construct several new kinds of Sidon spaces and Sidon sets by investigating some known results.Secondly,using these Sidon spaces,we will present a construction of cyclic subspace codes with cardinality τ,q^(n)-1/q-1 and minimum distance 2k-2,whereτis a positive integer.We further-more give some cyclic subspace codes with size 2τ·q^(n)-1/q-1 and without changing the minimum distance 2k-2.展开更多
We use the probabilistic method to prove that for any positive integer g there exists an infinite B2[g] sequence A = {ak} such that ak ≤ k^2＋1/g（log k）^1/g＋0（1） as k→∞. The exponent 2＋1/g improves the previo...We use the probabilistic method to prove that for any positive integer g there exists an infinite B2[g] sequence A = {ak} such that ak ≤ k^2＋1/g（log k）^1/g＋0（1） as k→∞. The exponent 2＋1/g improves the previous one, 2 ＋ 2/g, obtained by Erdos and Renyi in 1960. We obtain a similar result for B2 [g] sequences of squares.展开更多
文摘The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sidon series taking values in a Banach space: the summability on a set of positive measure implies the almost everywhere convergence; the contraction principle of Billard-Kahane remains true for Sidon series. As applications, they extend a uniqueness theorem of Zygmund concerning lacunary Fourier series and an analytic continuation theorem of Hadamard concerning lacunary Taylor series. Some of their results still hold for Sidon sets of second kind.
基金supported by the National Natural Science Foundation of China(Grant Nos.11771007,12171241).
文摘In this paper,we firstly construct several new kinds of Sidon spaces and Sidon sets by investigating some known results.Secondly,using these Sidon spaces,we will present a construction of cyclic subspace codes with cardinality τ,q^(n)-1/q-1 and minimum distance 2k-2,whereτis a positive integer.We further-more give some cyclic subspace codes with size 2τ·q^(n)-1/q-1 and without changing the minimum distance 2k-2.
基金Supported by project MTM 2008-03880 of MICINN (Spain) by the joint Madrid Region-UAM project TENU3 (CCG08-UAM/ESP-3906)
文摘We use the probabilistic method to prove that for any positive integer g there exists an infinite B2[g] sequence A = {ak} such that ak ≤ k^2＋1/g（log k）^1/g＋0（1） as k→∞. The exponent 2＋1/g improves the previous one, 2 ＋ 2/g, obtained by Erdos and Renyi in 1960. We obtain a similar result for B2 [g] sequences of squares.
