Spectral Analysis of Bounded Self-adjoint operators - A Linear Algebraic Approach

This thesis Entitled Spectral theory of bounded self-adjoint operators -A linear algebraic approach.The main results of the thesis can be classified as three different approaches to the spectral approximation problems. The truncation method and its perturbed versions are part of the classical linear algebraic approach to the subject. The usage of block Toeplitz-Laurent operators and the matrix valued symbols is considered as a particular example where the linear algebraic techniques are effective in simplifying problems in inverse spectral theory. The abstract approach to the spectral approximation problems via pre-conditioners and Korovkin-type theorems is an attempt to make the computations involved, well conditioned. However, in all these approaches, linear algebra comes as the central object. The objective of this study is to discuss the linear algebraic techniques in the spectral theory of bounded self-adjoint operators on a separable Hilbert space. The usage of truncation method in approximating the bounds of essential spectrum and the discrete spectral values outside these bounds is well known. The spectral gap prediction and related results was proved in the second chapter. The discrete versions of Borg-type theorems, proved in the third chapter, partly overlap with some known results in operator theory. The pure linear algebraic approach is the main novelty of the results proved here.

Development of a portable composite equipment for coastal fishery and hydrographic investigations

This thesis reports on the details of the works done to develop a complete system for acquisition of the important marine environmental parameters namely, current, current direction, salinity, temperature and depth. It encompaéps transducers,signalconditioners display arrangements and remote controlled multiplexer which constitue the system. The various associate instruentation and environmental requisites and problems have been discussed and solved to considerable extend. The design and development features of this composite system includes an integrated approach in order to make the final equipment to be simple, inexpensive and easy for operation from small and large boats. This could be achieved with the successful development of all required components with features matching between them, such as sensors, signals conditioners remote operated multiplexers, comon display methods, quick performance check and calibration methods. The major success rests on the development of sensors with excellent performance characteristics suitable for marine environment. out of the 5 sensors. that of current salinity and depth are quite noval types with specific advantages. The environmental effects have been eliminated to the required extend. The common signal conditioner for salinity, temperature and depth has noval design features for achieving simplicity, reliability and accomodating the three sensors of different functional requirements.