弗拉基米尔·安德烈耶维奇·斯捷克洛夫Vladimir Steklov

弗拉基米尔·安德烈耶维奇·斯捷克洛夫的父亲是一位神职人员，在下诺夫哥罗德神学院教授历史和希伯来语。他母亲一方的叔叔是一位著名的文学批评家。斯捷克洛夫继承了这些家族才能中的许多，他本人也颇有文学和音乐天赋。如果他没有以数学为职业，他完全可能以歌剧演唱家为业。

斯捷克洛夫十岁时进入下诺夫哥罗德的亚历山大学院。他在那里学习了八年，于1884年毕业。他进入莫斯科大学，但一年后转学到哈尔科夫大学。在那里他成为李雅普诺夫的学生，并在极为成功的大学学业之后于1887年毕业。斯捷克洛夫留在哈尔科夫大学，为成为大学教师而努力。1891年，他被任命为力学讲师，并为取得硕士学位而努力。

斯捷克洛夫的硕士论文研究的是在理想无粘性流体中运动的固体的方程。积分由这个问题产生的方程时有四种情形需要考虑，其中两种情形已由阿尔弗雷德·克莱布什于1871年解决。斯捷克洛夫在他的论文中解决了第三种情形，最后一种情形由斯捷克洛夫的导师李雅普诺夫于1893年解决。事实上，1893年正是斯捷克洛夫获得硕士学位的年份。然后，在1896年，斯捷克洛夫被任命为力学编外教授，并继续为他的博士学位论文而努力。

斯捷克洛夫的学位论文研究的是potential theory、静电学和水力学中出现的问题。他运用严格的数学分析将这类问题化为约翰·彼得·古斯塔夫·勒热纳·狄利克雷型的边值问题。斯捷克洛夫于1902年获得博士学位，同年，他的导师李雅普诺夫接受了圣彼得堡的聘任。斯捷克洛夫被任命为哈尔科夫大学应用数学讲席，该职位此前由李雅普诺夫空出。

斯捷克洛夫曾是哈尔科夫数学会的活跃成员，1891年任该学会秘书，1899年任副主席。1902年，即他被任命为应用数学讲席的那一年，斯捷克洛夫成为该学会主席，并担任此职直到1906年他迁往圣彼得堡接任那里的数学讲席。

关于斯捷克洛夫最引人注目的事实之一是，他坚持写日记约20年，逐日详细记录自己生活中的事件。我们对斯捷克洛夫生平的了解必定多于几乎任何其他数学家，但这些日记的意义远超出数学界，因为它们记录了俄国历史上一个特别动荡时期的种种事件。斯捷克洛夫每天的日记开头会记录上午10点的天气状况。他会记下温度、气压、云量、是否有雨或雪。然后每晚他会完成当天事件的记录。他详细记下当天收到和写出的信件。所有他拜访过或拜访过他的人都记录在案。最后一条记录是凌晨3点30分的天气状况，给出与上午10点条目相同的细节。

通过日记，我们知道斯捷克洛夫考核的每位学生在考试中表现如何。我们知道他每天讲的课。例如1908年9月10日：-

开始在大学讲授偏微分方程的积分。来的人相当多。讲课前，我说了几句关于亚历山大·科尔金[他于1908年9月8日去世]的话，并建议学生们起立以悼念他，他们当然照做了。

他关于偏微分方程积分的讲座课程是给三年级学生的，讲座一直持续到1909年4月。他在1909年4月25日记录道：-

结束了我关于方程积分的讲座。不知什么原因，学生们以掌声迎接我讲座的结束（他们是因为我讲完了而高兴吗？）。

斯捷克洛夫在俄罗斯政治情绪高涨的时期有着强烈的政治观点。他强烈反对沙皇政权，并同情进步学生。事实上，这使他在圣彼得堡成为一位非常受欢迎的老师，再加上他出色的讲课技巧，吸引了许多学生到数学物理系学习。他在圣彼得堡教过的学生中有亚历山大·弗里德曼、弗拉迪米尔·斯米尔诺夫和雅各布·塔马尔金。

1914年第一次世界大战爆发，带来了以沙皇为中心的爱国热情高涨，但斯捷克洛夫并不认同这种热情。当该城市的德文名称改为俄文名称彼得格勒时，斯捷克洛夫在1914年9月2日的日记中写道：-

圣彼得堡已奉帝国敕令改名为彼得格勒。我们的暴君只能做这些琐事……宗教游行和用一切可能的手段消灭俄罗斯人民。混蛋！好吧，你们等着。总有一天他们会吃苦头的！

1910年，斯捷克洛夫当选为俄罗斯科学院院士。然后在1919年，他成为科学院副院长。A.П. 尤什克维奇在[1]中写道：-

在内战、军事冲突、经济衰退和重建初期，他证明了自己是一位杰出的科学管理者。八年来，他不知疲倦地努力维持并后来扩大科学院的活动，并对其进行重组，以使科学与实际需求更紧密地结合起来。

1921年，斯捷克洛夫创立了物理与数学研究所，并担任所长直至1926年去世。1934年，该研究所分为物理研究所和数学研究所两个独立的研究所，数学研究所被命名为V 斯捷克洛夫数学研究所。

斯捷克洛夫对应用数学做出了许多重要贡献。除了上文提到的硕士论文和博士论文的工作外，他还将问题化为约翰·彼得·古斯塔夫·勒热纳·狄利克雷型的边值问题，其中拉普拉斯方程必须在曲面上求解。他写了General Theory of Fundamental Functions，其中考察了函数在无穷正交eigenfunctions系中的级数展开。事实上，“基本函数”这一术语源自儒勒·昂利·庞加莱，按今天的术语就是特征函数。

当然，斯捷克洛夫并不是第一个研究用无穷正交本征函数集展开级数的人，许多年前约瑟夫·傅里叶就已经考察过这种情况的一个特例。然而，斯捷克洛夫就这一主题发表了许多论文，这使他得以用一个一般理论来取代他人研究过的特例。他研究了马克-安托万·帕塞瓦尔关于Fourier series的等式在他的一般设定下的推广，并表明这是一个基本性质。总之，他的出版物列表中共有154项。

E A Tropp、V Ya 雅科夫·弗仑克尔和A D Chernin在[3]中写道，关于斯捷克洛夫：-

他不仅是一位杰出的数学家，而且有着异常鲜明的个性。……斯捷克洛夫留给我们的不仅有数学和数学物理的经典著作，还有一些具有文学价值的作品。这些包括他根据对美国之行的印象写成的《往返美国》（1925年），以及他关于罗蒙诺索夫和伽利略的著作。然而，他大量的文学遗产[他的日记]仍在等待出版和评注。

Vladimir Steklov's father was a clergyman who taught history and Hebrew at the Nizhni Novgorod seminary. His uncle on his mother's side of the family was a famous literary critic. Vladimir Steklov inherited many of these family talents and he himself had considerable literary and musical talents. Had he not made a career from mathematics he could well have made his profession as an opera singer.

Steklov entered the Alexander Institute in Nizhni Novgorod at the age of 10 years. He studied there for eight years graduating in 1884. He entered Moscow University but, after one year, he transferred to Kharkov University. There he became a student of Lyapunov and, after a highly successful university career, he graduated in 1887. Steklov remained at Kharkov University working towards becoming a university teacher. In 1891 he was appointed Lecturer in Mechanics and worked towards his Master's Degree.

For his Master's thesis Steklov worked on the equations of a solid body moving in an ideal non-viscous fluid. There were four cases to be considered in integrating the equations which arose from this problem, and two of these cases had been solved by Clebsch in 1871. Steklov solved the third case in his thesis, the final case being solved by Steklov's supervisor Lyapunov in 1893. In fact 1893 was the year that Steklov was awarded his Master's Degree. Then, in 1896, Steklov was appointed to an extraordinary professorship of mechanics and continued to work for his doctoral dissertation.

For his doctoral dissertation Steklov worked on problems that arose in potential theory, electrostatics and hydromechanics. He reduced problems of this type to boundary-value problems of Dirichlet type using rigorous mathematical analysis. Steklov was awarded his doctorate in 1902 and, in that year, his supervisor Lyapunov accepted an appointment at St Petersburg. Steklov was appointed to the Chair of Applied Mathematics at Kharkov University which Lyapunov had vacated.

Steklov had been an active member of the Kharkov Mathematical Society, serving the Society as secretary in 1891 and deputy chairman in 1899. In 1902, the year he was appointed to the Chair of Applied Mathematics, Steklov became chairman of the Society and held this post until 1906 when he moved to St Petersburg to take up the Chair of Mathematics there.

One of the most remarkable facts about Steklov was that he kept a diary for about 20 years, documenting in detail every day the events of his life. We must know more of Steklov's life than almost any other mathematician but the diaries are of interest far beyond the world of mathematics as they record events through a particularly dramatic period of Russian history. Steklov's entry for each day would begin with a record of the weather conditions at 10 a.m. He would record the temperature, atmospheric pressure, the degree of cloud cover, whether there was rain or snow. Then every night he would complete his record of the events of the day. He gave details of letters he had received and letters he had written that day. All those he visited or who visited him are recorded. The final entry was the weather conditions at 3.30 a.m. giving the same details as the 10 a.m. entry.

Through the diary we know how well every student that Steklov examined performed in their examination. We know the lectures that he gave on each day. For example on 10 September 1908:-

Began lecturing at the University on the integration of partial differential equations. There were quite a lot of people. Before the lecture I said a few words about A N Korkin [who died on 8 September 1908] and suggested that the students pay tribute to his memory by standing up, which of course they did.

His lecture course on the integration of partial differential equations was to third year students and the lectures went on until April 1909. He records on 25 April 1909:-

Finished my lectures on integration of equations. For some reason, the students greeted the end of my lecture with applause (were they happy that I had finished?).

Steklov had strong political views at a time when political feelings in Russia ran high. He was strongly against the Tsarist Regime and sympathised with progressive students. In fact this made him a very popular teacher at St Petersburg and, coupled with his excellent lecturing skills, brought many students to study at the Department of Mathematics and Physics. Among the students that he taught at St Petersburg were Friedmann, Smirnov and Tamarkin.

The outbreak of World War I in 1914 brought an upsurge of patriotic fervour centred on the tsar which was not shared by Steklov . When the German form of the city's name was changed to the Russian name of Petrograd, Steklov wrote in his diary entry of 2 September 1914:-

St Petersburg has been renamed Petrograd by Imperial Order. Such trifles are all our tyrants can do ... religious processions and extermination of the Russian people by all possible means. Bastards! Well, just you wait. They will get it hot one day!

In 1910 Steklov had been elected to the Russian Academy of Sciences. Then in 1919 he became vice-president of the Academy. A P Yushkevich writes in [1]:-

During the civil war, military conflicts, economic decline, and the early stages of reconstruction, he proved to be a brilliant scientific administrator. For eight years he worked tirelessly to maintain, and later to enlarge, the activity of the Academy and to reorganise it in order to bring science and practical requirements closer together.

In 1921 Steklov founded the Institute of Physics and Mathematics and served as its director until his death in 1926. In 1934 the Institute was split into two separate Institutes of Physics and of Mathematics and the Mathematics Institute was named the V A Steklov Mathematical Institute.

Steklov made many important contributions to applied mathematics. In addition to the work for his master's thesis and his doctoral thesis referred to above, he reduced problems to boundary value problems of Dirichlet type where Laplace's equation must be solved on a surface. He wrote General Theory of Fundamental Functions in which he examined expansions of functions as series in an infinite system of orthogonal eigenfunctions. In fact the term "Fundamental Functions", which is due to Poincaré, means eigenfunctions in today's terminology.

Steklov was not the first to examine series expansions in terms of infinite sets of orthogonal eigenfunctions, of course Fourier had examined a special case of this situation many years before. Steklov, however, produced many papers on this topic which led him to a general theory to replace the special cases examined by others. He studied a generalisation of Parseval's equality for Fourier series to his general setting showing this to be a fundamental property. In all his list of publications contains 154 items.

E A Tropp, V Ya Frenkel and A D Chernin, writing in [3], say of Steklov:-

He was not only an outstanding mathematician but also had an unusually bright personality. ... Steklov has bequeathed to us not only classical works in mathematics and mathematical physics, but also works of some literary merit. These include his book To America and back (1925), based on his impressions of his trip to the United States, as well as his books about Lomonosov and Galileo. Yet his vast literary legacy [his diary] is still waiting to be published and commented upon.