Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.

Extended spectral decompositions of the Renyi map

We present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map.

Submillimeter wave frequency selective surface with polarisation independent spectral responses

This paper reports the design, construction and electromagnetic performance of a new freestanding frequency selective surface (FSS) structure which generates coincident spectral responses for dual polarisation excitation at oblique angles of incidence. The FSS is required to allow transmission of 316.5 - 325.5 GHz radiation with a loss = 0.6 dB and to achieve = 30 dB rejection from 349.5 - 358.5 GHz. It should also exhibit crosspolarisation levels below -25 dB, all criteria being satisfied simultaneously for TE and TM polarisations at 45° incidence. The filter consists of two identical, 30 mm diameter, 12.5 ?m thick, optically flat, perforated metal screens separated by 450 ?m. Each of the ˜5000 unit cells contains two nested, short circuited, rectangular loop slots and a rectangular dipole slot. The nested elements provide a passband spectral response centred at 320 GHz in the TE and TM planes; the dipole slot increases the filter roll-off above resonance. The FSS was fabricated from silicon-on-insulator wafers using precision micromachining and plating processes including the use of Deep Reactive Ion Etching (DRIE) to pattern the individual slots and remove the substrate under the periodic arrays. Quasi–optical transmission measurements in the 250 – 360 GHz range yielded virtually identical copolarised spectral responses, with the performance meeting or exceeding the above specifications. Experimental results are in excellent agreement with numerical predictions.

A three-position spectral line survey of sagittarius B2 between 218 and 263 GHz. II. Data analysis

We present an analysis of the data from our Swedish-ESO Submillimetre Telescope molecular line survey in the 1.3 mm band of the N, M, and NW positions in the Sgr B2 molecular cloud. The line emissions from 42 molecular species, and some of their isotopomers, were analyzed assuming a single temperature and a homogeneous source. In cases where a source size much smaller than the antenna beam (23

Joined Spectral Trees for Scalable SPIHT-Based Multispectral Image Compression

In this paper, the compression of multispectral images is addressed. Such 3-D data are characterized by a high correlation across the spectral components. The efficiency of the state-of-the-art wavelet-based coder 3-D SPIHT is considered. Although the 3-D SPIHT algorithm provides the obvious way to process a multispectral image as a volumetric block and, consequently, maintain the attractive properties exhibited in 2-D (excellent performance, low complexity, and embeddedness of the bit-stream), its 3-D trees structure is shown to be not adequately suited for 3-D wavelet transformed (DWT) multispectral images. The fact that each parent has eight children in the 3-D structure considerably increases the list of insignificant sets (LIS) and the list of insignificant pixels (LIP) since the partitioning of any set produces eight subsets which will be processed similarly during the sorting pass. Thus, a significant portion from the overall bit-budget is wastedly spent to sort insignificant information. Through an investigation based on results analysis, we demonstrate that a straightforward 2-D SPIHT technique, when suitably adjusted to maintain the rate scalability and carried out in the 3-D DWT domain, overcomes this weakness. In addition, a new SPIHT-based scalable multispectral image compression algorithm is used in the initial iterations to exploit the redundancies within each group of two consecutive spectral bands. Numerical experiments on a number of multispectral images have shown that the proposed scheme provides significant improvements over related works.