An axiomatic approach to function spaces, spectral synthesis, and Luzin approximation / Lars Inge Hedberg, Yuri Netrusov.

Format:

Book

Author/Creator:

Hedberg, Lars Inge, 1935- author.

Netrusov, Yuri, author.

Series:

Memoirs of the American Mathematical Society ; Volume 188, Number 882.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 188, Number 882

Language:

English

Subjects (All):

Function spaces.

Spectral synthesis (Mathematics).

Approximation theory.

Physical Description:

1 online resource (112 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2007.

Language Note:

English

Summary:

The authors define axiomatically a large class of function (or distribution) spaces on $N$-dimensional Euclidean space. The crucial property postulated is the validity of a vector-valued maximal inequality of Fefferman-Stein type. The scales of Besov spaces ($B$-spaces) and Lizorkin-Triebel spaces ($F$-spaces), and as a consequence also Sobolev spaces, and Bessel potential spaces, are included as special cases. The main results of Chapter 1 characterize our spaces by means of local approximations, higher differences, and atomic representations. In Chapters 2 and 3 these results are applied to prove pointwise differentiability outside exceptional sets of zero capacity, an approximation property known as spectral synthesis, a generalization of Whitney's ideal theorem, and approximation theorems of Luzin (Lusin) type.

Contents:

""Contents""; ""Introduction. Notation""; ""Chapter 1. A Class of Function Spaces""; ""1.1. Definitions and Basic Properties""; ""1.2. Some Lemmas""; ""1.3. Proof of Theorem 1.1.14""; ""1.4. Some Lemmas on Orthogonalization""; ""1.5. Proof of Theorem 1.1.15""; ""1.6. Homogeneous Spaces""; ""1.7. Proof of Theorem 1.6.12""; ""1.8. Proof of Theorem 1.6.11""; ""Chapter 2. Differentiability and Spectral Synthesis""; ""2.1. Capacities and Differentials""; ""2.2. Spectral Synthesis""; ""2.3. Spectral Synthesis in Spaces of Distributions""; ""2.4. Invariant Subspaces and a Theorem of Whitney""

""Chapter 3. Luzin Type Theorems""""3.1. Luzin Approximation of Functions""; ""3.2. Luzin Approximation of Distributions""; ""Appendix. Whitney's Approximation Theorem in L[sub(p)](R[sup(N)]), p > 0""; ""Bibliography""

Notes:

"Volume 188, Number 882 (third of 4 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0486-9