We show that a Hilbert space bounded linear operator has an $m$-isometric lifting for some integer $m\ge 1$ if and only the norms of its powers grow polynomially. In analogy with unitary dilations contractions, we prove such operators also have

We introduce the concept of $k$-(semi)-dilation for Liouville domains, which is a generalization symplectic dilation defined by Seidel-Solomon. prove that existence property independent fillings asymptotically dynamically convex (ADC) manifolds. construct examples with $k$-dilations, but not $k-1$-dilations all $k\ge 0$. extract invariants taking value in $\mathbb{N} \cup \{\infty\}$ domains an...

We prove that any Parseval wavelet frame is the projection of an orthonormal wavelet basis for a representation of the Baumslag-Solitar group BS(1, 2) = 〈u, t | utu = t〉. We give a precise description of this representation in some special cases, and show that for wavelet sets, it is related to symbolic dynamics (Theorem 3.14). We show that the structure of the representation depends on the ana...

It is shown that polynomially bounded operators on Banach spaces have polynomially bounded dilations which have spectrum in the unit circle and are generalized scalar. The proof also yields a description of all compressions of generalized scalar operators with spectrum in the unit circle.

1 Basic definitions In this paper, we present a description of a collaboration with K. Guo, W. Lim, A. Savov and E. Wilson. We make use of the Fourier transform f → ˆ f that, for f ∈ L 1 (R n), is defined asˆf (ξ) = R n f (x) e −2πiξx dx. As is well-known, this operator has a unique extension to L 2 (R n) that is a unitary operator. In the following, we refer to the domain ofˆf as the " frequen...

We consider open symplectic manifolds which admit dilations (in the sense previously introduced by Solomon and the author). We obtain restrictions on collections of Lagrangian submanifolds which are pairwise disjoint (or pairwise disjoinable by Hamiltonian isotopies) inside such manifolds. This includes the Milnor fibres of isolated hypersurface singularities which have been stabilized (by addi...