Naslov
L^p(G)-Linear Independence and p-Zero Divisors

Autori
Slamić, Ivana

Izvornik
Mediterranean journal of mathematics (1660-5446) 15 (2018), 3; 120, 19

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
bracket function ; cyclic vector ; dual integrable representation ; l^p(G) -linear independence ; zero divisor

Sažetak
Let T be a dual integrable representation of a countable discrete LCA group G, acting on a Hilbert space H . We consider the problem of characterizing l^p(G) -linear independence ( p≠2 ) of the system {; ; ; T_kψ:k∈G}; ; ; for the given ψ∈H , which we previously studied in the context of the integer translates of a square integrable function. The extensions of the known results for translates to this setting are obtained using a slightly different approach, through which we show that, under certain conditions, this problem is related to the ‘Wiener’s closure of translates’ problem and the problem of the existence of p-zero divisors, arising around the zero divisor conjecture in algebra. Using this connection, we also obtain several improvements for the case of the integer translates.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA