Consider d commuting C0-semigroups (or equivalently: d-parameter C0-semigroups) over a Hilbert space for d∈N. In the literature (cf. [31], [27], [28], [24], [18], [26]), conditions are provided to classify existence of unitary and regular dilations. Some these require inspecting values semigroups, some provide only sufficient conditions, others involve verifying sophisticated properties generat...

among the therapeutic options for achalasia are pneumatic dilatation (pd), an appropriate long-term therapy, and botulinum toxin injection (bt) that is a relatively short-term therapy. this study aimed to compare therapeutic effect of repetitive pneumatic dilation with a combined method (botulinum toxin injection and pneumatic dilation) in a group of achalasia patients who are low responder to ...

Refinable functions and distributions with integer dilations have been studied extensively since the pioneer work of Daubechies on wavelets. However, very little is known about refinable functions and distributions with non-integer dilations, particularly concerning its regularity. In this paper we study the decay of the Fourier transform of refinable functions and distributions. We prove that ...

Proof. It would be easy to obtain these properties from the matrix form of U constructed in Sec. I.5.2, but we prefer to give a direct proof, independent of the particular realization of U . Part (i): To prove that L and L∗ are wandering subspaces, it suffices to show that UL0 ⊥L0 and UL0 ⊥ L0 for n = 1,2, . . .; by reason of symmetry it even suffices to consider one of these cases, say that of...

For any n-by-n complex matrix A and any k, 1 ≤ k ≤ n, let Λk(A) = {λ ∈ C : X∗AX = λIk for some n-by-k X satisfying X∗X = Ik} be its rank-k numerical range. It is shown that if A is an n-by-n contraction, then Λk(A) = ∩{Λk(U) : U is an (n + dA)-by-(n + dA) unitary dilation of A}, where dA = rank (In − A∗A). This extends and refines previous results of Choi and Li on constrained unitary dilations...

It was shown previously that the presence of endothelium modulates spontaneous vasomotion of small lymphatic vessels. In the present study, we aimed to elucidate the nature of endothelium-derived factors, produced in basal conditions and in response to agonists, that affect the smooth muscle tone of lymph microvessels in vitro. Afferent lymph microvessels were isolated from rat iliac lymph node...

Idiopathic polypoidal choroidal vasculopathy (IPCV) is a vascular malformation of the choroid, comprising a network of branching vessels of varying sizes that produce aneurysmal-like enlargements. This disease is generally observed in the peripapillary area, and less commonly as an isolated macular lesion. Frequently, the IPCV vascular network is associated with multiple episodic serosanguineou...