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Explore the spectral properties of Krein-Feller operators and their applications in fractal geometry through this hour-long conference talk presented at ICBS2025. Delve into the mathematical foundations of these specialized operators, examining how they arise naturally in the study of fractals and their geometric properties. Learn about the spectral analysis techniques used to understand these operators, including eigenvalue problems, spectral decomposition, and their relationship to fractal structures. Discover the connections between operator theory and fractal geometry, gaining insights into how Krein-Feller operators provide a powerful framework for analyzing complex geometric objects with self-similar properties.
