Fourier multipliers, symbols, and nuclearity on compact manifolds

• Published in: Journal d'analyse mathématique (Jerusalem) Vol. 135; no. 2; pp. 757 - 800
• Main Authors: Delgado, Julio, Ruzhansky, Michael
• Format: Journal Article
• Language: English
• Published: Jerusalem The Hebrew University Magnes Press 01.06.2018; Springer Nature B.V
• Subjects: Abstract Harmonic Analysis; Analysis; Dynamical Systems and Ergodic Theory; Fourier analysis; Functional Analysis; Hilbert space; Invariants; Mathematics; Mathematics and Statistics; Multipliers; Operators; Partial Differential Equations; Subspaces

The notion of invariant operators, or Fourier multipliers, is discussed for densely defined operators on Hilbert spaces, with respect to a fixed partition of the space into a direct sum of finite-dimensional subspaces. As a consequence, given a compact manifold M endowed with a positive measure, we...