7 papers
Categorified Spectral Sheaves and Homotopical Invariants for Noncommuting Operators
Shih-Yu Chang
Classical spectral theory gives a complete description of a single normal operator, but it fails for noncommuting operators, where no canonical joint spectrum or simultaneous diago…
Generalized Multiple Operator Integrals and Perturbation Theory for Operators with Continuous Spectra
Shih-Yu Chang
Operators with continuous spectra naturally arise in spectral theory, quantum mechanics, automorphic forms, and noncommutative geometry. However, analyzing such operators, particul…
Generalized Multiple Operator Integrals for Operators with Finite Dimensions
Shih-Yu Chang
Multiple Operator Integrals (MOIs) have played a foundational role in operator theory and functional calculus, particularly for analyzing Hermitian matrices via spectral decomposit…
Generalized Double Operator Integrals for Continuous Spectrum Operators
Shih-Yu Chang
Continuous spectrum operators (CSOs), characterized by spectra comprising continuous intervals rather than discrete eigenvalues, are pivotal in quantum mechanics, wave propagation,…
Generalized Double Operator Integrals: Finite Dimensions
Shih-Yu Chang
The Double Operator Integral (DOI) framework provides a powerful tool for analyzing perturbations and interactions between self-adjoint operators in functional analysis and spectra…
Tensor Unfolding Characterization
Shih-Yu Chang
Tensors play a pivotal role in the realms of science and engineering, particularly in the realms of data analysis, machine learning, and computational mathematics. The process of u…
Algebraic Connectivity Characterization of Ensemble Random Hypergraphs
Shih-Yu Chang
Random hypergraph is a broad concept used to describe probability distributions over hypergraphs, which are mathematical structures with applications in various fields, e.g., compl…