A very wide angle lens with a field of view 360°x180° - fisheye has been designed to be used in space environment. As case study, the is assumed mounted on spinning probe passing through comet’s tail. The lens, rotating comet coma, may map entire sky as viewed from interior tail, providing unprecedented data spatial distribution plasma and dust. Considering foreseen applications for radiation h...

For input/ouput (i/o) operators, an equivalence is shown between realizability by state space systems and the existence of analytic constraints on higher order derivatives of i/o signals. This provides a precise characterization of realizability, extending to the general analytic case previous work that dealt with the equivalence between algebraic realizability and algebraic i/o equations.

This note represents an approach to the abstract Fredholm theory of trace class (and more generally ~ = {A [ Tr(] A [ ~ ) < oo}) operators on a separable Hi lber t space, ~v{,. There are few new results here but there are a set of new proofs which we feel sheds considerable light on the theory discussed. In part i cular, we would emphasize our proof of Lidskii 's theorem (see Sect. 4): I t was ...

Let A be a linear bounded operator in a Hilbert space H, N(A) and R(A) its null-space and range, and A∗ its adjoint. The operator A is called Fredholm iff dim N(A) = dim N(A∗) := n < ∞ and R(A) and R(A∗) are closed subspaces of H. A simple and short proof is given of the following known result: A is Fredholm iff A = B + F , where B is an isomorphism and F is a finite-rank operator. The proof co...

I provide an algebraic formulation of classical field theories and use this to probe our interpretation of algebraic theories more generally. I show that the problem of unitarily inequivalent representations, as discussed in Ruetsche (2011), arises in classical theories just as in quantum theories, and I argue that this gives reason to not be a Hilbert Space Conservative when interpreting algeb...

In this paper, we show that for a hyponormal operator the analytic spectral subspace coincides with the algebraic spectral subspace. Using this result, we have the following result: Let T be a operator with property (δ) on a Banach space X and let S be a hyponormal operator on a Hilbert space H. Then every generalized intertwining linear operator θ : X → H for (S, T ) is continuous if and only ...

Let E be a modular elliptic curve over a totally real field. In [7, Chapter 8] the first author formulates a conjecture allowing the construction of canonical algebraic points on E by suitably integrating the associated Hilbert modular form. The main goal of the present paper is to obtain numerical evidence for this conjecture in the first case where it asserts something nontrivial, namely, whe...

Various algebraic structures have recently appeared in a parallel way in the framework of Hilbert schemes of points on a surface and respectively in the framework of equivariant K-theory [N1, Gr, S2, W], but direct connections are yet to be clarified to explain such a coincidence. We provide several non-trivial steps toward establishing our main conjecture on the isomorphism between the Hilbert...