Luzin (18831February 9, 950-1February 2, 950) Luzin, nikolayevich, Soviet mathematician. 1883 was born in Tomsk on February 9th, and 1950 died in Moscow on February 2nd. 1906 graduated from Moscow university, and studied in France twice in 1905 and 19 10, and met a group of famous French scholars at that time, which had an important influence on his future scientific research. 19 16 received a doctorate in pure mathematics. 19 17 became a professor at Moscow university. 1927 was elected as an academician of the Soviet academy of sciences, and 1929 was an academician. 1928 was elected as the vice chairman of the 8th International Congress of Mathematicians.
Chinese name: Luzin.
Nikolayevich Luzin
Nationality: former Soviet Union
Place of birth: Tomsk, former Soviet Union
Date of birth:1883 65438+February 9th.
Date of death:1February 2, 950
Occupation: Mathematician
Graduate school: Moscow University,
Main achievements: Luzin is the core figure of Moscow School of Mathematics.
Masterpieces: Studied function testability and measure theory, description function theory, projection set.
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Luzin is the core figure of the Moscow School of Mathematics. Studied function testability and measure theory, description function theory, projection set. Luzin also made important contributions to the analysis of boundary properties of functions and the unique determination of functions by boundary values. Great achievements have been made in the fields of differential geometry and differential equations. On the problem of surface deformation, in a sense, he got the final result. He also established a series of important theorems in analytic set theory.
Luzin conjecture
A famous problem in Fourier series theory. In a paper published in 19 13, the Russian mathematician η η Luzin put forward the following conjecture: the Fourier series of the square integrable function in the interval 0,2π converges to 0,2π almost everywhere. After the efforts of many mathematicians for more than half a century, this conjecture was finally confirmed by Swedish mathematician L Carlson with a very profound mathematical method.
Fourier series theory originated from the study of heat conduction at the beginning of19th century. The central question is: What kind of function can be expressed by its Fourier series? With the establishment of Lebesgue measure and Lebesgue integral theory, people gradually pay attention to the convergence of Fourier series, which can be seen almost everywhere. 1906, the P.J.L diagram was first proved.
After Luzin's conjecture was published, it attracted the attention of many first-class mathematicians in the world. In the long 53 years, this conjecture can neither be confirmed nor denied. But around it, some important achievements have been made from both positive and negative aspects. In 1923, α η Andre Andrey Kolmogorov constructed an integrable function whose Fourier series diverged almost everywhere. 1926, he discovered an integrable function whose Fourier series diverged everywhere. But these two integrable functions are not square integrable. Therefore, Luzin's conjecture is undeniable. The work of Andre Andrey Kolmogorov, γ A Seliverstov and A Plaisner in 1925 is close to Luzin's conjecture. They further simplified W(n) to logn, but this is still far from confirming Luzin's conjecture. There was no significant progress in the next 40 years. Based on the above two counterexamples of Andre Andrey Kolmogorov, there is a tendency to deny Luzin's conjecture among quite a number of influential mathematicians. For example, in 1946, at the seminar on mathematical problems held to commemorate the 200th anniversary of the founding of Princeton University in the United States, A. Zangemon believed that according to historical experience, guessing in trigonometric series theory often failed. He pointed out that it is not clear whether even the Fourier series of a continuous function must have a convergence point. He considered the problem from the perspective of denying Luzin's conjecture. Since then, Luzin conjecture has generally become two positive and negative questions with tendentiousness: ① Is there a continuous function whose Fourier series diverges on a positive measure point set? ② Does the Fourier series of all continuous functions converge almost everywhere? Focusing the problem on the continuous function reflects a certain degree of inclination, that is, the original Luzin conjecture may not hold. However, it proves that the change of the Luzin issue has not made much progress.