Gokhberg, Israel Tsudikovich

Early years

Israel Gokhberg was born in the colony of Tarutino in southern Bessarabia in the family of Tsudik Itsikovich Gokhberg (1900-1942) and Khai Isaakovna Gokhberg (1904-1984), the owner of a small printing house (accountant by profession) and midwife ^{[4] [5]} . This settlement - now the district center of Tarutinsky district of Odessa region of Ukraine - in those years was inhabited mainly by Swabian Germans ; a quarter of the population were Jews . Gokhberg studied at the Jewish school in Tarutino , then at the Romanian gymnasium in Orhei . With the advent of Soviet power in 1940, his father was arrested ^[6] and died in Pechlag in 1942 (rehabilitated posthumously in 1968 ) ^[7] . At the beginning of World War II, the thirteen-year-old Izya with his mother and seven-year-old sister ^[8] were evacuated to the Voroshilovsky district of the Frunze region of Kyrgyzstan , where he graduated from high school at the Vasilyevsky state farm. An important role in Hochberg's mathematical education was played by his school teacher Modest Semyonovich Shumbarsky, who had graduated from Warsaw University before the war and defended his thesis under the guidance of the famous Polish topologist Karol Borsuk ^[9] .

In 1946 , Gokhberg entered the Kyrgyz State Pedagogical Institute , where after the first year of study he became a Stalin scholarship holder . After the second course, in 1948, he returned to Moldova and settled in Chisinau , where he graduated with honors from the Physics and Mathematics Department of Chisinau State University . During the years of study, V. A. Andrunakievich (student of the professor of Moscow State University A. G. Kurosh ), D. L. Pikus (student of the professor of Moscow State University V. F. Kagan ) and I. A. Itskovich (student of the professor of LGU ) had a significant influence on the beginning mathematician S. G. Mikhlin ). Despite scientific success and a diploma with honors, Hochberg was denied entry to graduate school and in 1951 he was sent to work at the Soroka Teachers Institute.

Scientific Activities in Moldova

In the same 1951, he published his first scientific work in the field of functional analysis and already from Forty continued to publish in the country's central mathematical publications (Doklady Akademii Nauk SSSR , Uspekhi Matematicheskikh Nauk, Mathematical Digest, and Izvestia Akademii Sciences of the MSSR "). In 1953, Gokhberg was transferred to the Pedagogical Institute in Balti , where he received the post of assistant professor and then head of the department of mathematics. While in Balti , externally defended his thesis at the Leningrad State Pedagogical Institute . A.I. Herzen (opponents - G.P. Akilov and S.G. Mikhlin , 1954 ) and began scientific cooperation with the leading Soviet mathematician Mark Grigorievich Krein , who was dismissed from Odessa State University in the midst of the campaign against rootless cosmopolitanism . Collaboration with Crane, who became the teacher and scientific mentor of the young mathematician, led to two joint monographs and the defense of a doctoral dissertation at M.V. Lomonosov Moscow State University in 1964 (opponents S.G. Mikhlin , M.A. Naimark and G. E. Shilov ) under the review of the Institute of Applied Mathematics of the Academy of Sciences of the USSR (under the direction of M.V. Keldysh )

In 1959, Gokhberg was invited to Chisinau , where he headed the department of functional analysis at the Institute of Mathematics of the Academy of Sciences of the Moldavian SSR (then the Moldavian branch of the USSR Academy of Sciences). He taught at the Department of Mathematics and Computer Science, Chisinau State University. During these years, he, together with M.G. Krein, achieved serious results in the development of the theory of linear non-self-adjoint operators (published as a separate monograph in 1965 ), as well as the theory of Fredholm operators and their applications, which put him forward as one of the largest Soviet mathematicians. Starting from the International Mathematical Congress ( 1966 ) in Moscow, Gokhberg and Crane spoke at mathematical conferences and published on behalf of the mathematician GoCra. In 1967, the second joint monograph by Hochberg and Crane, “Theory of Volterra Operators in Hilbert Space and its Application,” was published.

In 1966 he received the title of professor, became a member of the Moscow Mathematical Society and now heads the sector of functional analysis and approximate methods of the Institute of Mathematics of the Academy of Sciences of the MSSR. In 1970 , he was elected a corresponding member of the Moldavian Academy of Sciences (lost membership in 1974 due to repatriation to Israel ). By 1974, Gokhberg (with co-authors) had published 136 scientific papers and 7 monographs, prepared several doctors of sciences, including leading Moldovan mathematicians such as A. S. Markus , I. A. Feldman , N. Ya. Krupnik , A. A. Sementsul , O. I. Soibelman and about 30 candidates of sciences ( L. S. Goldenstein , Jürgen Laiterer ^[10] , R. V. Duduchava , V. A. Zolotarevsky , G. I. Russu, V. P. Soltan other). Further scientific and teaching activities in Moldova, however, ran into insurmountable difficulties. Participation in international conferences, despite personal invitations, becomes impossible; under the pretext of, allegedly, his illness, beginners are being appointed to his place in the delegations. In 1974 , after a refusal of an exit visa and a year without work, he manages to leave for Israel, and he and his family (mother, wife Bella Yakovlevna, two daughters) settle in a suburb of Tel Aviv ^[11] .

In Israel

Immediately upon arrival, Israel, Hochberg became a professor at Tel Aviv University (professor emeritus since 1996 ) and the Weizmann Institute of Science in Rehovot (1975-1983). In 1981-1998 - Head of the Department of Mathematical Analysis and Theory of Operators named after Nathan and Lily Silver, Tel Aviv University. From 1983 to 1998, he was also a professor at the Free University in Amsterdam (professor emeritus from 1998 ), a visiting professor at a number of universities in the USA and Canada . Foreign member of the Royal Academy of Arts and Sciences of the Netherlands (since 1985 ). Honorary Doctor of the Higher Technical School in Darmstadt (1997), Vienna University (2001), Western University in Timisoara (Doctor Honoris Causa, 2002), State University of Moldova (Chisinau, Doctor Honoris Causa, 2003 ), Alecu Russo State University in Balti (Doctor Honoris Causa, 2003 ^[12] ) and the Israel Institute of Technology (Technion, Haifa , 2008), an honorary member of the Society for Industrial and Applied Mathematics, SIAM (2009) ^[13] .

He was awarded the Landau Prize in Mathematics (1976), the Rothschild Prize in Mathematics (1985), the Humboldt (1992), the Hans Schneider Linear Algebra (1994), and the M. G. Kerin Prize (2008) ^[14] . In 1996, Gokhberg was reinstated as a corresponding member of the Academy of Sciences of Moldova.

The scientific productivity of Hochberg is very great. As of July 2007 (according to the Science Citation database) he (with co-authors) had published about 500 articles and 25 monographs in English , some of which were translated into other languages ​​( Japanese , French , Hungarian , Spanish and German ). Gochberg was also the founder (1978) and editor-in-chief of the monthly magazine Integral Equations and Operator Theory (Integral Equations and Operator Theory), published in Basel . He edited the series of books “Operator Theory: Advances and Applications” ( Operator Theory: Successes and Applications ) - 180 volumes have been published to date. A series of scientific collections was published on the basis of the anniversary of international conferences on the sixtieth anniversary ( Calgary , 1988), seventy ( Beer-Sheva , 1998) and seventy-fifth ( Cagliari , 2003 ) mathematics. Hochberg's 80th Anniversary Symposium was held in Williamsburg ( Virginia , USA ) in August 2008 ; based on the materials of the symposium, a collective collection of scientific papers “Israel Gohberg and Friends” was published.

I. Ts. Gokhberg is one of the founders and life president of the International Workshops on Operator Theory and Applications, or IWOTA . IWOTA organizes international conferences on the theory of operators and their applications (18 such conferences by 2007 ). Gokhberg was the organizer of 11 so-called "greenhouse readings" - international conferences at the University of Tel Aviv dedicated to the memory of the mathematician Otto Teplitz , who, after escaping from Nazi Germany, lived with his family in Jerusalem .

Among the students of Gokhberg at Tel Aviv University - Leiba Rodman , Israel Coltracht, Nir Cohen, Vadim Olshevsky, Asher Ben-Artsi, Daniel Alpay and others.

• The theory of Fredholm operators and its applications.
• One-dimensional and multidimensional singular integral operators; symbol as a Gelfand transform, or finite-dimensional representations in Banach algebras .
• Wiener - Hopf equations , infinite Toeplitz matrices, and factorization of matrix functions.
• General theory of non-self-adjoint operators and its applications, trace and determinant in the infinite-dimensional case.
• Projection methods for the Wiener - Hopf equations and their discrete analogues.
• Fast inversion algorithms , Hochberg-Semenzul formulas, Hochberg-Heinig formulas, and Hochberg-Krupnik formulas for inverting finite Otto Toeplitz matrices and their continuous analogues.
• Factorization of operators and characteristic functions, factorization of operator functions, local principle.
• Linear system input / output, implementation and method of state spaces.
• Tape method of extrapolation and interpolation and their application, the principle of maximum entropy .
• Interpolation of matrix functions with metric constraints, applications to problems of systems theory and control and control theory.
• Theory of holomorphic operator functions, local / global method, Oka-Grawert principle.
• Numerical methods for matrices, fast algorithms for structural matrices, matrices with a display-cement structure, quasi-separable and separable representations of matrices.
• Indefinite linear algebra.
• Theory of partially defined matrices.

• Wife (since 1956) - Bella Yakovlevna Gokhberg, endocrinologist.
  • Daughters - Tsviya (Viliya, 1956) and Ioannina (1960).

Books in Russian

• Gokhberg, I. Ts., Kerin, M. G. Introduction to the theory of linear non-self-adjoint operators. Moscow: Science, 1965. Publications in English: Providence: American Mathematical Society, 1969, 1978, 1983, 1988. In French: Paris : Dunod, 1971.
• Gokhberg, I. Ts., Boltyansky, V. G. Theorems and problems of combinatorial geometry ( full text here ). Moscow: Nauka, 1965. English edition: Cambridge : Cambrige University Press, 1985. In Hungarian: Budapest : Tankönyvkiadó, 1970. In German: Berlin : Deutsche Verlag der Wissenschaften, 1972.
• Gokhberg, I. Ts., Kerin, M. G. The theory of Volterra operators in Hilbert space and its application. Moscow: Science, 1967. In English: Providence : American Mathematical Society, 1970.
• Gokhberg, I. Ts., Feldman, I. A. Projection methods for solving the Wiener-Hopf equations. Chisinau: Shtiintsa, 1967.
• Gokhberg, I. Ts., Boltyansky, V. G. Partitioning of figures into smaller parts ( full text here ). Moscow: Science, 1971. In English: Chicago : University of Chicago Press, 1980. In Hungarian: Budapest: Tankönyvkiadó, 1976. In Spanish: Moscow: World, 1973.
• Gokhberg, I. Ts., Feldman, I. A. Convolution equations and projection methods for solving them. Moscow: Science, 1971. In English: Providence: American Mathematical Society, 1974. In German: Berlin: Akademie-Verlag, 1974.
• Gokhberg, I. Ts., Krupnik, N. Ya. Introduction to the theory of one-dimensional singular integral operators. Chisinau: Stiince, 1973. In German: Basel : Birkhauser Verlag, 1979.

Books in English

• Introduction to the Theory of Linear Nonselfadjoint Operators (translated from Russian). Providence : American Mathematical Society, 1969. Reprints: 1978, 1983, 1988. In French: Paris : Dunod, 1971.
• Theory and Applications of Volterra Operators in Hilbert Space (with M. G. Crane, translation from Russian). Providence: American Mathematical Society, 1970.
• Convolution Equations and Projection Methods for Their Solution (with I. A. Feldman). Providence: American Mathematical Society, 1974.
• Recent Progress in Operator Theory. New York : Springer-Verlag, 1980.
• The decomposition of figures into smaller parts (with V. G. Boltyansky, translation from Russian). Chicago : University of Chicago Press, 1980.
• Basic Operator Theory (with Seymour Goldberg). Basel: Birkhäuser, 1981.
• Factorization of matrix functions and singular integral operators (c K. Clancey). Basel - Boston - Stuttgart : Birkhäuser Verlag, 1981.
• Matrix Polynomials (with Peter Lancaster and Leiba Rodman). Berlin : Academie Verlag, 1982; reprinted - Philadelphia : The Society for Industrial and Applied Mathematics (SIAM), 2009.
• Matrices and Indefinite Scalar Products. Basel: Birkhäuser, 1984.
• Results and Problems in Combinatorial Geometry (with V. G. Boltyansky, translation from Russian). Cambridge : Cambridge University Press, 1985.
• Constructive Methods of Wiener-Hopf Factorization. Basel: Birkhäuser, 1986.
• Invariant Subspaces of Matrices With Applications (Canadian Mathematical Society Series of Monographs and Advanced Texts). John Wiley & Sons, 1986; Reprinted - Philadelphia: SIAM, 2006.
• Topics in Operator Theory and Interpolation. Basel: Birkhäuser, 1988.
• Topics in Interpolation Theory Of Rational Matrix Valued functions. New York: Springer-Verlag, 1988.
• Orthogonal Matrix-Valued Polynomials and Applications. New York: Springer-Verlag, 1988.
• An Introduction to Operator Polynomials. Basel: Birkhäuser, 1989.
• Interpolation of Rational Matrix Functions (with Joseph A. Ball and Leiba Rodman). Basel: Birkhäuser, 1990.
• One Dimensional Linear Singular Integral Equations: Introduction (with N. Ya. Krupnik). Basel: Birkhäuser, 1991.
• One-Dimensional Linear Singular Integral Equations: General Theory and Applications (second part, N. Ya. Krupnik). New York: Springer-Verlag, 1992.
• Time-Variant Systems and Interpolation. New York: Springer-Verlag, 1992.
• Continuous and Discrete Fourier Transforms. New York: Springer-Verlag, 1992.
• Contributions to Operator Theory and its Applications: The Tsuyoshi Ando Anniversary Volume (with Takayuki Furuta). Basel: Birkhäuser, 1993.
• New Aspects in Interpolation and Completion Theories. New York: Springer-Verlag, 1993.
• Classes of Linear Operators (with Seymour Goldberg and MA Kaashoek). Basel: Birkhäuser, 1993.
• Classes of Linear Operators, in two volumes (with M. Kaashok). Basel: Birkhäuser, 1993.
• Matrix and Operator Valued Functions. New York: Springer-Verlag, 1994.
• Operator Theory and Boundary Eigenvalue Problems. Basel: Birkhäuser, 1995.
• Indefinite Linear Algebra and Applications (with Peter Lancaster and Leiba Rodman). Basel: Birkhäuser, 1995.
• Partially Specified Matrices and Operators: Classification, Completion, Applications (with MA Kaashoek and Frederik Van Schagen). Basel: Birkhäuser, 1995.
• Differential and Integral Operators. New York: Springer-Verlag, 1998.
• Traces and Determinants of Linear Operators (with N. Ya. Krupnik and Seymour Goldberg). Basel: Birkhäuser, 2000.
• Basic Operator Theory (with Seymour Goldberg). Basel: Birkhäuser, 2001.
• Orthogonal Systems and Convolution Operators (with Robert L. Ellis). Basel: Birkhäuser, 2003.
• Basic Classes of Linear Operators (with Seymour Goldberg and Marinus A. Kaashoek). Basel: Birkhäuser, 2004.
• Indefinite Linear Algebra and Applications (with Peter Lancaster and Leiba Rodman). Basel: Birkhäuser, 2005.
• Invariant Subspaces of Matrices with Applications (Classics in Applied Mathematics series, with Peter Lancaster and Leiba Rodman, reprint). Basel: Birkhäuser, 2006.
• Factorization of Matrix and Operator Functions: The State Space Method (with Harm Bart, Marinus A. Kaashoek and André CM Ran). Basel: Birkhäuser, 2007.
• A State Space Approach to Canonical Factorization with Applications: Preliminary Entry 332 (with Harm Bart, Marinus A. Kaashoek and André CM Ran). Basel: Birkhäuser, 2008.
• Holomorphic Operator Functions of One Variable and Applications: Methods from Complex Analysis in Several Variables (with Jürgen Leiterer). Operator Theory: Advances and Applications, Vol. 192. Basel: Birkhäuser, 2009.
• Separable Type Representations of Matrices and Fast Algorithms. Volume 1: Basics. Completion Problems. Multiplication and Inversion Algorithms (with Yuli Eidelman and Iulian Haimovici). Basel: Birkhäuser, 2013.
• Separable Type Representations of Matrices and Fast Algorithms. Volume 2: Eigenvalue Method (with Yuli Eidelman and Iulian Haimovici). Basel: Birkhäuser, 2014.

Edited by I. Ts. Gokhberg

Since the late 1980s, under the general editorship of prof. Hochberg Swiss publishing house "Birkhäuser" ( Basel - Boston - Stuttgart ) published a book series "Operator Theory Advances and Applications". It published materials from international conferences, monographs, reviews and scientific reports. The number of voluminous (up to 1000 pages) volumes of the series during the life of I. Ts. Gokhberg reached almost two hundred.

Anniversary editions in honor of I. Ts. Gokhberg

• The Gohberg Anniversary Collection: Topics in Analysis and Operator Theory (Calgary Conference and Matrix Theory Papers in honor of I. Gohberg, two volumes, 1064 p.). Edited by Harry Dym, Seymour Goldberg, Marinus A. Kaashoeck and Peter Lancaster. Basel: Birkhäuser, 1989.
• Recent Advances in Operator Theory and Its Applications: The Israel Gohberg Anniversary Volume. Edited by Marinus A. Kaashoek, Sebastiano Seatzu and Cornelis van der Mee. Basel: Birkhäuser, 2005.
• Israel Gohberg and Friends: On the Occasion of his 80th Birthday. Edited by Harm Bart, Thomas Hempfling and Marinus A. Kaashoek. Basel: Birkhäuser, 2008.
• Topics in Operator Theory. Volume 1: Operators, Matrices and Analytic Functions. Edited by Leiba Rodman, Joseph A. Ball, Vladimir Bolotnikov, J. William Helton, Ilya M. Spitkovsky. Базель: Birkhäuser, 2010. ^[5]

• The Bart-Gohberg-Kaashoek-Van Dooren Theorem
• Лекция проф. Гохберга «Бесконечные системы линейных уравнений» (видео RealPlayer)
• Photo album
• Фотографии с одной из конференций по случаю 70-летия И. Ц. Гохберга в Университете Бен-Гуриона
• Фотогалерея в Университете «Алеку Руссо» в Бельцах
• Семейные фотографии
• Биографические данные в Архиве истории математики МакТутора
• Индекс цитирования (ISI) Гохберга
• Выступление в 1973 году (недоступная ссылка)
• Семья Гохберг (недоступная ссылка)
• 1960-е гг. (inaccessible link)