2003/01/31 by A. G. Ramm, А. Г. Рамм, Ramm, A. G.
Engineering · Mathematics · #30D20 #35J05 #35J10 #35R25 #41-XX #65M30 #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #Elasticity and Material Modeling #FOS: Mathematics #Numerical methods in inverse problems #math.CA #msc:30D20 #msc:35J05 #msc:35J10 #msc:35R25 #msc:41-XX #msc:65M30
paper · pdf · doi:10.48550/arxiv.math/0301380
arxiv created 2003/01/31 · openalex publication_date 2003/01/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Several questions of approximation theory are discussed: 1) can one approximate stably in L^∞ norm f^′ given approximation fδ, ∥ fδ- f ∥L^∞ < δ, of an unknown smooth function f(x), such that ∥ f^′ (x) ∥L^∞ ≤ m1? 2) can one approximate an arbitrary f ∈ L2(D), D ⊂ \Rn, n ≥ 3, is a bounded domain, by linear combinations of the products u1 u2, where um ∈ N(Lm), m=1,2, Lm is a formal linear partial differential operator and N(Lm) is the null-space of Lm in D, 3) can one approximate an arbitrary L2(D) function by an entire function of exponential type whose Fourier transform has support in an arbitrary small open set? Is there an analytic formula for such an approximation? N(Lm) := \w: Lm w=0 \hboxin\ D\?