Modal stabilizability and spectral synthesis
We propose a modification of the golden ratio algorithm for solving pseudomonotone equilibrium problems with a Lipschitz-type condition in Hilbert spaces. A new non-monotone stepsize rule is used in the method. Without such an additional condition, the theorem of weak convergence is proved. Furthermore, with strongly pseudomonotone condition, the $R$-linear convergence rate of the method is established. The results obtained are applied to a variational inequality problem, and the convergence rate...
In a series of papers beginning in the late 1990s, Michael Lacey and Christoph Thiele have resolved a longstanding conjecture of Calderón regarding certain very singular integral operators, given a transparent proof of Carleson’s theorem on the almost everywhere convergence of Fourier series, and initiated a slew of further developments. The hallmarks of these problems are multilinearity as opposed to mere linearity, and especially modulation symmetry. By modulation is meant multiplication by characters...
We prove that for symbols in the modulation spaces , p ≥ q, the associated multilinear pseudodifferential operators are bounded on products of appropriate modulation spaces. In particular, the symbols we study here are defined without any reference to smoothness, but rather in terms of their time-frequency behavior.