Analysis of Spectral Projectors in One-dimensional Domains
نویسنده
چکیده
In this paper we analyze a class of projection operators with values in a subspace of polynomials. These projection operators are related to the Hubert spaces involved in the numerical analysis of spectral methods. They are, in the first part of the paper, the standard Sobolev spaces and, in the second part, some weighted Sobolev spaces, the weight of which is related to the orthogonality relation satisfied by the Chebyshev polynomials. These results are used to study the approximation of a model fourth-order problem.
منابع مشابه
Analysis of High-order Approximations by Spectral Interpolation Applied to One- and Two-dimensional Finite Element Method
The implementation of high-order (spectral) approximations associated with FEM is an approach to overcome the difficulties encountered in the numerical analysis of complex problems. This paper proposes the use of the spectral finite element method, originally developed for computational fluid dynamics problems, to achieve improved solutions for these types of problems. Here, the interpolation n...
متن کاملFurther properties of a pair of orthogonal projectors
Representing two orthogonal projectors on a finite dimensional vector spaces (i.e., Hermitian idempotent matrices) as partitioned matrices turns out to be very powerful tool in considering properties of such a pair. The usefulness of this representation is discussed and several new characterizations of a pair of orthogonal projectors are provided, with particular attention paid to the spectral ...
متن کاملFree and Forced Transverse Vibration Analysis of Moderately Thick Orthotropic Plates Using Spectral Finite Element Method
In the present study, a spectral finite element method is developed for free and forced transverse vibration of Levy-type moderately thick rectangular orthotropic plates based on first-order shear deformation theory. Levy solution assumption was used to convert the two-dimensional problem into a one-dimensional problem. In the first step, the governing out-of-plane differential equations are tr...
متن کاملAn extension theorem for finite positive measures on surfaces of finite dimensional unit balls in Hilbert spaces
A consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable Hilbert space. It is proved, through a Kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the Hilbert space. As an application, this will naturally accomplish the work of Kante...
متن کاملOperator and Spectral Theory
This lecture is a complete introduction to the general theory of operators on Hilbert spaces. We particularly focus on those tools that are essentials in Quantum Mechanics: unbounded operators, multiplication operators, self-adjointness, spectrum, functional calculus, spectral measures and von Neumann’s Spectral Theorem. 1.1 Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . ...
متن کامل