Manuscript Topics

Functional analysis is a source of knowledge to approach both linear and nonlinear problems in the theory of partial differential equations and systems. Further, it deals with the qualitative analysis of linear transformations on infinite dimensional spaces, endowed with a norm. Therefore, it plays a key-role in representation theory of many real-life problems modelled as complex systems. This issue can be enriched if attention is shifted to probability theory on infinite dimensional spaces which are required to study generalized stochastic processes, hence infinite dimensional generalized functions.

The aim of this special issue is to focus on the recent developments in the theory of functional analysis and infinite dimensional spaces, which are basically designed for solving differential problems and analyzing complex systems. Hence it is aimed to provide a platform for reflection and exchange of ideas, within which to discuss current literature.

This special issue is devoted to collect original and new results, as well as review papers. In details, the scope is to cover topics that include normed spaces, completeness and Banach spaces, linear and self-adjoint operators, operator norms, Hilbert spaces, functionals, Lebesgue measures, integrability, dual spaces, the Hahn-Banach theorem, spectral theory.

Potential topics include but are not limited to:
• Linear and nonlinear differential equations and systems.
• Variational formulation of boundary value problems in Sobolev spaces.
• Existence, multiplicity and regularity of solutions to evolution equations.
• Spectral decomposition of compact self-adjoint operators.
• Convolution and regularization of functionals in Lᵖ spaces.
• Ergodic theory and applications.
• Measure and integration.

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