Anisotropic Mixed-Norm Banach Spaces : Functional Analytic Structures, Operator Theory, Sobolev-Type Domains, Duality, And Isomorphism Of The Discrete Bravais Tori

Key Points

• This research aims to establish a unified framework for anisotropic mixed-norm Banach spaces and their properties.
• Rigorous analysis of functional analytic structures in $ extbf{L}^p( extbf{R}^d, oldsymbol{ ext{}} \\ell_q^m( extbf{C}))$ and $ extbf{L}^p( extbf{R}^d, \\ell_q^{2m}( extbf{R}))$.
• Investigation of operator theory related to position and Laplacian operators.
• Examination of dual representation and isomorphism of discrete Bravais tori.
• Established theoretical foundations for the study of non-Hermitian transport in quantum physics.
• Integrated Baire-Steinhaus theorems and topological concepts relevant to the framework.
• Demonstrated the significance of Sobolev-type domains in the studied Banach spaces.