02682nam a22004935i 4500 978-3-031-63242-6 DE-He213 20251030112652.0 cr nn 008mamaa 240726s2024 sz | s |||| 0|eng d 9783031632426 978-3-031-63242-6 10.1007/978-3-031-63242-6 doi QA299.6-433 PBK bicssc MAT034000 bisacsh PBK thema García García, Antonio. author. aut http://id.loc.gov/vocabulary/relators/aut 81343 The Use of Frames in Sampling Theory [electronic resource] / by Antonio García García. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XVI, 302 p. 14 illus., 12 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda RSME Springer Series, 2509-8896 ; 14 - What does sampling theory mean? -- Basic sampling theory -- Sampling in shift-invariant subspaces -- A review on Kramer sampling theorem -- A generalized sampling theory -- Finite frames related to sampling in finite-dimensional U-invariant subspaces -- Sampling in shift-invariant-like subspaces of Hilbert-Schmidt operators. This book provides a comprehensive review of regular sampling based on frame theory in a separable Hilbert space. Thus, sampling theory has common features in almost all situations: classical theory, Kramer sampling theory, and finite sampling or sampling Hilbert–Schmidt operators. In addition, the transversality of sampling theory with other mathematical fields appears, in an easy way. The first three chapters of the book can be used as an introduction to sampling theory, while the rest of the chapters are addressed to introduce the interested reader in the research on the topic. Mathematical analysis. 64178 Analysis. SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031632419 Printed edition: 9783031632433 Printed edition: 9783031632440 RSME Springer Series, 2509-8896 ; 14 72920 https://doi.org/10.1007/978-3-031-63242-6 ZDB-2-SMA ZDB-2-SXMS 61940 61940