Fourier Series with Respect to General Orthogonal Systems
Fourier Series with Respect to General Orthogonal Systems
复制标题
一般正交系统的傅立叶级数
DOI：
10.1007/978-3-642-66056-6
复制
发表时间：
1975
影响因子：
1.3
通讯作者：
H. J. Christoffers
中科院分区：
文献类型：
--
作者：
A. Olevskiǐ;B. Marshall;H. J. Christoffers
术语。初步信息。--I.傅里叶级数在经典意义下的收敛。有界系统的勒贝格函数。-1。基本不等式。-2。勒贝格函数的对数增长。傅立叶级数的散度。-3.系数递减的级数。-4.推广，反例，问题-5.正交化算子的稳定性.-II.系数几乎处处收敛的条件.-1.S类？.-2.Garsia定理.-3.完备系统中收敛级数的系数.-4.函数系统到ONS的推广.-III.完备系统的性质与Haar系统的作用.-1.基本构造.-2.发散傅立叶级数.-3.函数空间中的基和傅里叶级数的主数.-4.连续函数的傅里叶系数.-5.更多的结果关于Haar系统。-IV。来自L2的级数和来自空间LP的傅里叶级数的特性。-1。矩阵AK。-2。勒贝格函数和几乎处处收敛。-3。来自不同类别的函数的傅里叶级数的收敛。-4。傅里叶级数的和。-5。休伯特空间中的条件基。
Terminology. Preliminary Information.- I. Convergence of Fourier Series in the Classical Sense. Lebesgue Functions of Bounded Systems.- 1. The Fundamental Inequality.- 2. The Logarithmic Growth of the Lebesgue Functions. Divergence of Fourier Series.- 3. Series with Decreasing Coefficients.- 4. Generalizations, Counterexamples, Problems.- 5. The Stability of the Orthogonalization Operator.- II. Convergence Almost Everywhere Conditions on the Coefficients.- 1. The Class S?.- 2. Garsia's Theorem.- 3. The Coefficients of Convergent Series in Complete Systems.- 4. Extension of a System of Functions to an ONS.- III. Properties of Complete Systems the Role of the Haar System.- 1. The Basic Construction.- 2. Divergent Fourier Series.- 3. Bases in Function Spaces and Majorants of Fourier Series.- 4. Fourier Coefficients of Continuous Functions.- 5. Some More Results about the Haar System.- IV. Series from L2 and Peculiarities of Fourier Series from the Spaces Lp.- 1. The Matrices Ak.- 2. Lebesgue Functions and Convergence Almost Everywhere.- 3. Convergence of Fourier Series of Functions from Various Classes.- 4. Sums of Fourier Series.- 5. Conditional Bases in Hubert Space.