Asymptotics of eigenvalues of high-order differential operator with discrete self-similar weight

2010/09/27 by Alexander Vladimirov, Vladimirov, A. A., I. A. Sheipak +1
Engineering · Mathematics · #34B09 #34L20 #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Material Science and Thermodynamics #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1009.5335

openalex publication_date 2010/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The spectral problem for the high order differential operator with singular weight is considered. If the weight is a generalized derivative of self-similar function with zero spectral degree the asymptotics of eigenvalues is obtained. They are proved to have exponential growth and depend on the order of differential operator and self-similarity parameters.

Related

• Asymptotics of eigenvalues of Sturm--Liouville problem with discrete self-similar weight
• Method of oscillation and spectral problem for four-order differential operator with self-similar weight
• Self-similar functions in L₂[0,1] and Sturm--Liouville Problem with singular indefinite weight
• Spectral data asymptotics for the higher-order differential operators with distribution coefficients
• Indefinite Sturm--Liouville problem for some classes of self-similar singular weights