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Displaying 41 –
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We consider the following Hamiltonian equation on the Hardy space on the circle,where is the Szegő projector. This equation can be seen as a toy model for totally non dispersive evolution equations. We display a Lax pair structure for this equation. We prove that it admits an infinite sequence of conservation laws in involution, and that it can be approximated by a sequence of finite dimensional completely integrable Hamiltonian systems. We establish several instability phenomena illustrating...
Let M and N be nonzero subspaces of a Hilbert space H satisfying M ∩ N = {0} and M ∨ N = H and let T ∈ ℬ(H). Consider the question: If T leaves each of M and N invariant, respectively, intertwines M and N, does T decompose as a sum of two operators with the same property and each of which, in addition, annihilates one of the subspaces? If the angle between M and N is positive the answer is affirmative. If the angle is zero, the answer is still affirmative for finite rank operators but there are...
We prove the existence of the density of states of a local, self-adjoint operator determined by a coercive, almost periodic quadratic form on . The support of the density coincides with the spectrum of the operator in .
For any holomorphic function F in the unit polydisc Uⁿ of ℂⁿ, we consider its restriction to the diagonal, i.e., the function in the unit disc U of ℂ defined by F(z) = F(z,...,z), and prove that the diagonal mapping maps the mixed norm space of the polydisc onto the mixed norm space of the unit disc for any 0 < p < ∞ and 0 < q ≤ ∞.
We compute the essential Taylor spectrum of a tuple of analytic Toeplitz operators on , where D is a strictly pseudoconvex domain. We also provide specific formulas for the index of provided that is a compact subset of D.
In this paper, it is proved that the Fourier integral operators of order , with , are bounded from three kinds of Hardy spaces associated with Herz spaces to their corresponding Herz spaces.
Let be a positive Borel measure on the complex plane and let with . We study the generalized Toeplitz operators on the Fock space . We prove that is bounded (or compact) on if and only if is a Fock-Carleson measure (or vanishing Fock-Carleson measure). Furthermore, we give a necessary and sufficient condition for to be in the Schatten -class for .
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