QUANTUM APPROXIMATION ON ANISOTROPIC SOBOLEV AND HÖLDER-NIKOLSKII CLASSES

• Published in: Taiwanese journal of mathematics Vol. 16; no. 1; pp. 71 - 88
• Main Author: Ye, Peixin
• Format: Journal Article
• Language: English
• Published: Mathematical Society of the Republic of China 01.02.2012
• Subjects: Approximation; Banach space; Coordinate systems; Cubes; Determinism; Embeddings; Mathematical functions; Quantum computers; Sobolev spaces

We estimate the quantum query error of approximation to functions from the anisotropic Sobolev class ℬ ( W p r ( [ 0 ,   1 ] d ) ) and the Hölder-Nikolskii class ℬ ( H p r ( [ 0 ,   1 ] d ) ) in theLq ([0, 1] d ) norm for all 1 ≤p, q≤ ∞. It turns out that for the class ℬ ( W p r ( [ 0 ,   1 ] d ) )...