Interpolation of linear operators is the direction of functional analysis . considering Banach spaces as elements of a certain category . The general theory of interpolation of linear operators was developed, starting in 1958, in the works of S. G. Kerin [1] [2] , J.-L. Lyons , J. Petre. It has numerous applications in the theory of Fourier series [3] , in approximation theory [4] , in the theory of partial differential equations.
Notes
- ↑ S. Kerin, On an interpolation theorem in operator theory, DAN SSSR 130, 3 (1960), 491 - 494
- ↑ Krein S.G. , Petunin Yu.I. "Scales of Banach spaces" , UMN 21: 2 (128) (1966), 89 - 169
- ↑ Crane, 1978 , p. 233.
- ↑ Crane, 1978 , p. 284.
Literature
- Krein S. G. , Petunin Yu. I. , Semenov E. M. Interpolation of linear operators. - M .: Nauka, 1978.- 400 p.