Functional Analytic

Functional analytic methods are increasingly applied to solve complex problems in various scientific domains by leveraging the power of infinite-dimensional spaces and operator theory. Current research focuses on developing novel algorithms, such as those based on Fourier transforms and orthogonal polynomials, for tasks like symbolic regression, probability density estimation, and anomaly detection in functional data (e.g., time series). These approaches offer advantages in handling high-dimensional data and complex relationships, leading to improved accuracy and efficiency compared to traditional methods, with applications ranging from machine learning to engineering diagnostics.