In mathematics, in the area of complex analysis, Carlson's theorem is a uniqueness theorem which was discovered by Fritz David Carlson. Informally, it states that two different analytic functions which do not grow very fast at infinity can not coincide at the integers.

Carleson's theorem is a fundamental result in mathematical analysis establishing the pointwise almost everywhere convergence of Fourier series of L 2 functions, proved by Lennart Carleson .

2003年7月1日 · Carleson's Theorem asserts the pointwise convergence of Fourier series of square integrable functions. We give a complete proof, following joint work of the author and C. Thiele. Over 20 exercises are also detailed. We also discuss the derviation of …

4 天之前 · If f (z) is regular and of the form O (e^ (k|z|)) where k<pi, for R [z]>=0, and if f (z)=0 for z=0, 1, ..., then f (z) is identically zero.

2014年7月17日 · For a function in $L_2 (0,2\pi)$ its trigonometric Fourier series converges almost everywhere. This was stated as a conjecture by N.N. Luzin [1] and proved by L. Carleson [2]. The statement of Carleson's theorem is also valid for functions in $L_p$ for $p>1$ (see [3]).

Chapter 1 Basic Probability Theory In this chapter we introduce the mathematical framework of probability theory, which makes it possible to reason about uncertainty in a principled way using set theory.

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1. Carlos concluded that the longest side in 𝛥 is ̅̅̅̅ after finding that the angle opposite to ̅̅̅̅ is the largest angle. What theorem did Carlos use to make such conclusion? A. Triangle Inequality Theorem 1 ( 𝑠→ 𝑎) B. Triangle Inequality Theorem 2 ( 𝑎→ 𝑠)

2023年10月1日 · Carlos Simpson, A Giraud-type characterization of the simplicial categories associated to closed model categories as ∞ \infty-pretopoi (arXiv:math/9903167) On secondary characteristic classes: Jaya N. Iyer, Carlos Simpson, Regulators of canonical extensions are torsion: the smooth divisor case (arXiv:0707.0372)

2003年11月16日 · View a PDF of the paper titled Computer theorem proving in math, by Carlos T. Simpson View PDF Abstract: We give an overview of issues surrounding computer-verified theorem proving in the standard pure-mathematical context.