On approximation of functions of two variables by sums of the form \(\varphi (x) + \psi (y)\) in \(L_ p\) spaces \((1\leq p\leq\infty )\)

DOI10.1007/BF02674899zbMath0870.41019OpenAlexW2043450783MaRDI QIDQ1363467

A. L. Garkavi

Publication date: 7 August 1997

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02674899

zbMATH Keywords

Banach spacesbest approximationproximinal subspace\(L_ p\) spaceslighting bolt

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Best approximation, Chebyshev systems (41A50) Functions of several variables (26B99) Approximation by arbitrary linear expressions (41A45)

Cites Work

• Approximation by a sum of two algebras. The lightning bolt principle
• Approximation theory in tensor product spaces
• On existence of a best uniform approximation of a function in two variables by the sums \(\varphi (x)+ \psi (y)\)
• On approximation theory and functional equations
• On the approximation of a function of several variables by the sum of functions of fewer variables
• On Proximinality in L 1 (T × S)
• A generalization of a problem of Steinhaus
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