Fourier-analysis, selfadjointness

Isogeometric analysis: vibration analysis, Fourier and wavelet spectra

This paper presents the Fourier and wavelet characterization of vibratio...

Fourier Analysis

(1.1) |〈u,v〉| ≤ ‖u‖ ‖v‖. An outline of a proof of this fundamental inequality, when V = R and ‖ · ‖ is the standard Eucledian norm, is given in Exercise 24 of Section 2.7 of [1]. We will give a proof in the general case at the end of this section. LetW be an n dimensional subspace of V and let P : V 7→W be the corresponding projection operator, i.e. if v ∈ V then w = Pv ∈W is the element in W w...

Fourier Analysis

Fourier Analysis and Wavelet Analysis

658 NOTICES OF THE AMS VOLUME 44, NUMBER 6 I n this article we will compare the classical methods of Fourier analysis with the newer methods of wavelet analysis. Given a signal, say a sound or an image, Fourier analysis easily calculates the frequencies and the amplitudes of those frequencies which make up the signal. This provides a broad overview of the characteristics of the signal, which is...

Meshless analysis of casting process considering non-Fourier heat transfer

Casting is considered as a major manufacturing process. Thermal analysis of a solidifying medium is of great importance for appropriate design of casting processes. The conventional governing equation of a solidifying medium is based on the Fourier heat conduction law, which does not account for the phase-lag between the heat flux and the temperature gradient. In this paper, the concept of phas...