In these notes, we present a number of interesting and diverse applications of the Spectral Theorem for Normal Operators. These include a Spectral Mapping Theorem for Normals Operators, a Spectral Characterization of Algebraic Operators, von Neumann’s Mean Ergodic Theorem, Pathconnectivity of the Group of Invertible Operators, and some Polynomial Approximation Results for Operators.

Multispectral classification, one of the most commonly used methods for mapping burned areas, is based on the spectral properties of different classes of interest and employs special algorithms designed to perform various types of spectral analysis. However, the use of these classifications has been repeatedly reported to create confusion between burned areas and nonvegetation categories, espec...

We explore the technique of controlling synthesis using an instrumental or other sound source. The range of spectra available from the sound source, and also that available from the synthesis technique, are estimated and the first is mapped to the second. Suitable synthesis parameters for the synthesis algorithms are found by searching a database of known output spectra. A simple experiment ill...

Three-dimensional spectroscopy of extended sources is typically performed with dedicated integral field spectrographs. We describe a method of reconstructing full spectral cubes, with two spatial and one spectral dimension, from rastered spectral mapping observations employing a single slit in a traditional slit spectrograph. When the background and image characteristics are stable, as is often...

Spectral reflectance in the visible and near-infrared offers a rapid and inexpensive technique for determining the mineralogy of samples and obtaining information on chemical composition. Absorption-band parameters such as the position, depth, width, and asymmetry of the feature have been used to quantitatively estimate composition of samples from hyperspectral field and laboratory reflectance ...

Let T=H+iK be hyponormal and Q be a strictly monotone increasing continuous function on s(H ). We define ~ Q(T ) by ~ Q(T )=Q(H )+iK. In this paper, we show that if z is an isolated eigenvalue of ~ Q(T ), then the corresponding Riesz projection is self-adjoint. Also we introduce Xia spectrum and study the existence of an invariant subspace of an operator ~ Q(T ).

We propose in this note a spectral method on triangles based on a new rectangle-to-triangle mapping, which leads to more reasonable grid distributions and efficient implementations than the usual approaches based on the collapsed transform. We present the detailed implementation for spectral approximations on a triangle and discuss the extension to spectral-element methods and three dimensions.

Spectral printing aims to achieve an illuminant-invariant match between the original and the reproduction. Due to limited printer spectral gamuts, an errorless spectral reproduction is mostly impossible, and spectral gamut mapping is required to reduce perceptual errors. The recently proposed paramermismatch-based spectral gamut mapping (PMSGM) strategy minimizes such errors. However, due to it...

Spectral imaging has been widely developed over the last ten years for archiving cultural heritage. It can retrieve spectral reflectance of each scene pixel and provide the possibility to render images for any viewing condition. A new spectral reconstruction method, the matrix R method, can achieve high spectral and colorimetric accuracies simultaneously for a specific viewing condition. Althou...

In this paper, accuracy improvement in the displacement measurement systems using Dopplerinterferometry method is presented. The cross-talk error reduction methods are also discussed. Based on the mentioned method, a new nano-displacement measurement system is designed. In the designed system, the signal to leakage ratio for moving targets in the range of -20m/s to +20m/s is increased to 55dB. ...