### 数学代写|复变函数作业代写Complex function代考|Math 213A

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|复变函数作业代写Complex function代考|First Steps in Schur Analysis

After the defense of our joint dissertation on problems of the filter theory of multidimensional stationary sequences in December 1983, Bernd Fritzsche and I decided to aim our future research at the analytic foundation of prediction theory of multivariate stationary sequences. Against this background, we took up intense studies of the trend-setting works of the Soviet school (Kolmogorov, Rozanov, Matveev) as well as of American scholars (Wiener, Masani, Helson, Lowdenslager). During this process, we became aware of V. P. Potapov’s fundamental work [45] about the multiplicative structure of $J$-contractive matrix functions for the first time and we began to study the basics of $J$-theory systematically. Our choice of this research field was considerably encouraged by $P$. R. Masani. During Masanis’s visit of Leipzig University in May 1986 we had profound discussions about the state of prediction theory at that time and its prospects. P. R. Masani revealed to us that in collaboration with Norbert Wiener, following the works $[43,44,50,51]$, further research on an application of the results of V. P. Potapov in prediction theory was planned. However, the realization of this intention became unattainable due to Norbert Wiener’s death on March 18,1964 . Without Norbert Wiener P. R. Masani was reluctant to tackle this project and he turned towards a systematic elaboration of the theory of measures with orthogonal values in a Hilbert space or rather of the theory of orthoprojector-valued measures. P. R. Masani encouraged us to get in direct touch with the students of V. P. Potapov, who had passed away in the year 1980 . V. P. Potapov had been employed at the FTINT (Russian abbreviation for B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine in Kharkov) during the last period of his life (1976-1980) and he was able to contribute significantly to the popularization of $J$-Theory. In particular, he managed to assemble a group of exceedingly committed mathematicians in Kharkov who devoted themselves with inequalities to matricial versions of classical interpolation and moment problems. Among others, I. V. Kovalishina, V. E. Katsnelson, V. K. Dubovoy, L. B. Golinskii, I. V. Mikhailova, and Yu. M. Dyukarev belonged to this circle of mathematicians. In the summer of 1986 , Bernd Fritzsche and I decided to invite one representative of the circle of the above mentioned mathematicians to a month-long work visit at Leipzig University in the year \$1987.

## 数学代写|复变函数作业代写Complex function代考|Viktor Emmanuilovich’s First Visit to Leipzig

Over the course of planning the research activities for the year 1989 in fall 1988 , Bernd Fritzsche and I intended to hold a week-long international seminar on Schur analysis. This request was complied with by the administration of the Center for Theoretical Sciences (NTZ). The week from October 16-20, 1989 was specified as the date of the event. In connection with this seminar, we requested a 3-week stay for V. E. at Leipzig University. This request was granted as well. On September 23 , 1989 , he arrived in Leipzig. Aged 46 years it was his very first travel abroad. At the beginning of his stay it was unforeseeable that during his visit certain incidents would happen in Leipzig, which should stir up the political situation in the GDR significantly. V. E. became an eye-witness of the massive Monday protests in the city center of Leipzig on both October 9th and Uctober 16th that set the decay of the GDR in motion. Within a personal evaluation of these events, he reasoned that the reunification of Germany was the only consequence that seemed logical. We ourselves considered his prognosis very utopian at the time. History proved, though, that he had predicted everything completely correctly. Less than 1 year later, on October 3, 1990, the reunification of Germany was in fact enforced. During the first 3 weeks of his stay in Leipzig, Bernd and I had profound mathematical discussions with him, where he drew our attention to central problems in Schur analysis and, moreover, imparted to us fundamental aspects of the research of the Kharkov school. At that time, his lectures were held in Russian and I acted as interpreter into German for the audience (Fig. 2). At the end of his stay in Leipzig, the INTSEM (International Seminar) on Schur Analysis took place. It was P. R. Masani who had suggested the event during his first visit to Leipzig in 1986. The aim of this seminar was to gather leading specialists from the East and the West working on Schur analysis. This goal was successfully pursued. Among the Western participants were P. R. Masani, A. Dijksma, H. S. V. de Snoo, S. Hassi, and others. The list of Soviet participants included I. V. Kovalishina, V. E. Katsnelson, V. K. Dubovoy, Yu. L. Shmulyan, and I. M. Spitkovskii (Fig. 3). On October 17, 1989, the second day of the seminar, Mark Grigorevich Krein, one of the greatest mathematicians of the twentieth century, who had made fundamental contributions to Schur analysis and numerous other fields passed away. For this reason, D. Z. Arov has not been able to come to Leipzig for the seminar in time. He arrived on October 21 st, that is, 1 day after the end of the seminar. Following the seminar, it was intended that he would stay in Leipzig for another 3 weeks. During this time, the foundation for a long-term scientific collaboration with D. Z. Arov was set.

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