Annihilating sets for the short time Fourier transform

Multilinear Fourier multipliers related to time–frequency localization

“…For arbitrary ψ ∈ L 2 (R d ) we use an approximation argument and (1). The sets satisfying the hypothesis of the previous theorem are thin at infinity in the sense of [21,Definition 3.2]. We observe that for a set A ⊂ R 2d with finite measure, the conclusion of Theorem 3.11 follows from Proposition 3.6.…”

Supports of Representations in the Cohen Class

“…It is well-known that W (f ) cannot be compactly supported even in the case that f belongs to S (R d )\{0} (see [8]). The situation is completely different for representations in Cohen class, as the following example shows.…”

“…Recently the study of uncertainty principles for time-frequency representations has received the attention of several authors (see for instance [3,7,8,15,16]). It is usually assumed that any time-frequency representation should satisfy some appropriate version of the uncertainty principle.…”

Windowed-Wigner Representations in the Cohen Class and Uncertainty Principles

“…Another relevant issue in time-frequency analysis is the presence of some forms of uncertainty principle associated with each representation. The literature on this subject is very vast, we follow in particular the lines of [10] and we prove in Section 4 different uncertainty principles for Wig ψ and Wig * ψ , in the form of properties concerning the support of the representations. Finally in the same section we extend in a natural way the "duality" between Wig ψ and Wig * ψ to a duality between general representations in the Cohen class.…”