An abstract Logvinenko-Sereda type theorem for spectral subspaces

The Logvinenko-Sereda Theorem for the Fourier-Bessel transform

Abstract. The aim of this paper is to establish an analogue of Logvinenko-Sereda’s theorem for the Fourier-Bessel transform (or Hankel transform) Fα of order α > −1/2. Roughly speaking, if we denote by PWα(b) the Paley-Wiener space of L -functions with FourierBessel transform supported in [0, b], then we show that the restriction map f → f |Ω is essentially invertible on PWα(b) if and only if Ω...

A Bollobás-type theorem for affine subspaces

A nonlinear spectral theorem for abstract Nemitsky operators

An abstract standardisation theorem

The standardisation theorem is a key theorem in the-calculus. It implies that any normal form can be reached by the normal order (leftmost outermost) strategy. The theorem states that any reduction may be rearranged in a top-down and left-to-right order. This also holds in orthogonal term rewriting systems (TRS), although the left-to-right order is more subtle. We give a new presentation of the...

Sum Formula for Maximal Abstract Monotonicity and Abstract Rockafellar’s Surjectivity Theorem

In this paper, we present an example in which the sum of two maximal abstract monotone operators is maximal. Also, we shall show that the necessary condition for Rockafellar’s surjectivity which was obtained in ([19], Theorem 4.3) can be sufficient.