A Blind Source Separation Technique for Document Restoration

Hahn-Banach and Sandwich Theorems for Equivariant Vector Lattice-Valued Operators and Applications

“…where b y denotes the constant function defined on G which assumes the value b y . From (9) we deduce that h(J f ) = J hf , that is the assertion.…”

“…Among the consequences of this theorem we recall, for instance, the Fencheltype duality theorem which has several applications in minimax theorems, in particular in Economics and stochastic programming (see, e.g., [3, 13, 37-39, 43, 44]) and image and/or document reconstruction (see, e.g., [2,4,9,15,16,19,20]).…”

Hahn-Banach-Type Theorems and Subdifferentials for Invariant and Equivariant Order Continuous Vector Lattice-Valued Operators with Applications to Optimization

“…The Hahn-Banach theorem is one of the most important results in Functional Analysis, and has played a fundamental role, both because it has several deep theoretical consequences and since there have been a lot of studies and applications in various branches of Mathematics and other sciences, e.g., Subdifferential Calculus, Optimization, Operations Research, Numerical Analysis, Differential Equations, Calculus of Variations, Measure theory, Probability, Image Restoration (see, e.g., [2,3,8,11,12,16]). Some other related topics are, for instance, amenable (semi)groups, invariant and equivariant functionals, which are widely used in Probability, Statistics and Machine Learning (see, e.g.…”