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Operators in the Theory of Walsh-Fourier Series,In this chapter, and the next, we shall obtain several results about Walsh-Fourier series by using properties of operators which take one space of measurable functions to another. We begin with definitions and some simple properties of the class of operators we wish to use.敬礼 发表于 2025-3-29 06:34:53
Operators in the Theory of Walsh-Fourier Series,In this chapter, and the next, we shall obtain several results about Walsh-Fourier series by using properties of operators which take one space of measurable functions to another. We begin with definitions and some simple properties of the class of operators we wish to use.Awning 发表于 2025-3-29 08:06:46
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Generalized Multiplicative Transforms,Let 1 ≤ . < ∞. A complex valued function .(.) is said to belong to .(0, ∞) if ∫.|.(.)|. > ∞. The norm of .(.) in the space .(0, ∞) will be denoted by ǁ.ǁ. and is defined bywall-stress 发表于 2025-3-29 16:21:48
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Lacunary Subsystems of the Walsh System,The Rademacher system, {.(.)} = {., . = 0,1,…, which was used to define the Walsh system (see §1.1), is a typical example of what is called a . of the Walsh system. We shall study these systems in the next several sections.