Modulus of continuity for superlacunar trigonometric series and continuity of Gaussian stationary random processes

2021/10/05 by Maria Rosaria Formica, Formica, M. R., E. Ostrovsky +3
Computer Science · Mathematics · #Advanced Data Compression Techniques #Advanced Research in Science and Engineering #FOS: Mathematics #Probability (math.PR) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2110.01998

openalex publication_date 2021/10/05 · openalex created_date 2021/10/11 · openalex updated_date 2026/07/28

Abstract

We deduce bilateral interrelations between Fourier coefficients for lacunar trigonometric series and modulus of their continuity. We obtain also as an application some conditions for continuity and discontinuity for Gaussian periodic stationary random centered processes.

Related

• CLT for L^p moduli of continuity of Gaussian processes
• A canonical form for Gaussian periodic processes
• Precise Limit Theorems for Lacunary Series
• Sharp moduli of continuity for Gaussian fields and stochastic PDEs via correlation bounds
• Exact uniform modulus of continuity for q-isotropic Gaussian random fields