Related Experiment Video
Updated: Jun 20, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
Published on: August 19, 2021
The spectral side of Arthur's trace formula
Tobias Finis1, Erez M Lapid, Werner Müller
1Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, D-40225 Düsseldorf, Germany.
Abstract:
The trace formula is one of the most important tools in the theory of automorphic forms. It was invented in the 1950's by Selberg, who mostly studied the case of hyperbolic surfaces, and was later on developed extensively by Arthur in the generality of an adelic quotient of a reductive group over a number field. Here we provide an explicit expression for the spectral side, improving Arthur's fine spectral expansion. As a result, we obtain its absolute convergence for a wide class of test functions.
Related Concept Videos
Attenuated Total Reflectance (ATR) Infrared Spectroscopy: Overview
The ATR process begins by directing a beam...
Parseval's Theorem
Interestingly, Parseval's theorem also holds for the trigonometric form of the Fourier series, which expresses a...
Emission Spectra
Parseval's Theorem for Fourier transform
To understand Parseval's theorem, it is essential to first comprehend how signal energy is typically calculated. When considering a signal's...
Aliasing
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
Phasor Arithmetics
When the derivative of a sinusoid is taken in the time domain, it transforms into its corresponding phasor multiplied by j-omega (jω) in the phasor domain, where j is the imaginary unit, and ω is the angular frequency.

