Donoho-Logan large sieve principles for modulation and polyanalytic Fock spaces

We obtain estimates for the Lp-norm of short-time Fourier transform (STFT) functions in modulation spaces, providing information about concentration on a given subset R2, leading to deterministic guarantees perfect reconstruction using convex optimization methods. More precisely, we large sieve inequalities Donoho-Logan type, but instead localizing signals regions T×W time-frequency plane intertwine time and frequency, localize representation terms sets Δ with arbitrary geometry. At technical level, since there is no proper analogue Beurling's extremal function STFT setting, introduce new method, which rests combination an argument similar Schur's test extension Seip's local reproducing formula general Hermite windows. When windows are functions, formulas polyanalytic Fock spaces lead explicit constant and, as byproduct, f∈L2(R) from its values discs.