Collected Papers

ISBN-13: 9784431550501 / Angielski / Miękka / 2015 / 633 str.

Kosaku Yosida; Kiyosi Ito

Opis

Kosaku Yosida, born on February 7, 1909, was brought up in Tokyo. Having majored in Mathematics at University of Tokyo, he was appointed to Assistant at Osaka University in 1933 and promoted to Associate Professor in 1934. He re ceived the title of Doctor of Science from Osaka University in 1939. In 1942 he was appointed to Professor at Nagoya University, where he worked very hard with his colleagues to promote and expand the newly established Department of Mathe matics. He was appointed to Professor at Osaka University in 1953 and then to Professor at University of Tokyo in 1955. After retiring from University of Tokyo in 1969, he was appointed to Professor at Kyoto University, where he also acted as Director of the Research Institute for Mathematical Sciences. He retired from Kyoto University in 1972 and worked as Professor at Gakushuin University until 1979. Yosida acted as President of the Mathematical Society of Japan, as Member of the Science Council of Japan, and as Member of the Executive Committee of the International Mathematical Union. In 1967 he received the Japan Academy Prize and the Imperial Prize for his famous work on the theory of semigroups and its applications. In 1971 he was elected Member of the Japan Academy. Yosida went abroad many times to give series of lectures at mathematical in stitutions and to deliver invited lectures at international mathematical symposia."

Spis treści

I. Meromorphic Functions and Ordinary Differential Equations.- A remark to a theorem due to Halphen [3]+.- A generalisation of a Malmquist’s theorem [4].- On the distribution of ?-points of solutions for linear differential equation of the second order [6].- A note on Riccati’s equation [7].- On the characteristic function of a transcendental meromorphic solution of an algebraic differential equation of the first order and of the first degree [8].- On algebroid solutions of ordinary differential equations [9].- On a class of meromorphic functions [10].- A theorem concerning the derivatives of meromorphic functions [12].- On the groups of rationality for linear differential equations [13].- On Titchmarsh-Kodaira’s formula concerning Weyl-Stone’s eigenfunction expansion [62].- A note on Malmquist’s theorem on first order algebraic differential equations [102].- II. Topological Groups and Lie Groups.- On the group embedded in the metrical complete ring [14].- On the group embedded in the metrical complete ring. II [15].- A note on the continuous representation of topological groups [16].- A theorem concerning the semi-simple Lie groups [17].- A problem concerning the second fundamental theorem of Lie [18].- A remark on a theorem of B. L. van der Waerden [19].- On the exponential-formula in the metrical complete ring [20].- A note on the differentiability of the topological group [21].- A characterisation of the adjoint representations of the semisimple Lierings [22].- Numbers in brackets refer to the Bibliography at the end of this volume.- On the fundamental theorem of the tensor calculus [23].- On the duality theorem of non-commutative compact groups [46].- Equivalence of two topologies of Abelian groups (with T. Iwamura) [52].- III. Ergodic Theory.- Abstract integral equations and the homogeneous stochastic process [24].- Mean ergodic theorem in Banach spaces [25].- Application of mean ergodic theorem to the problems of MarkofTs process (with S. Kakutani) [26].- Operator-theoretical treatment of the MarkofTs process [28].- Operator-theoretical treatment of Markoffs process. II [30].- BirkhotTs ergodic theorem and the maximal ergodic theorem (with S. Kakutani) [31].- Asymptotic almost periodicities and ergodic theorems [32].- Mark off process with an enumerable infinite number of possible states (with S. Kakutani) [33].- Ergodic theorems of Birkhoff-Khintchine’s type [34].- The Markoff process with a stable distribution [35].- An abstract treatment of the individual ergodic theorem [36].- Operator-theoretical treatment of Markoff’s process and mean ergodic theorem (with S. Kakutani) [38].- Simple Markoff process with a locally compact phase space [56].- Ergodic theorems for pseudo-resolvents [86].- IV. Spectral Theorems, Vector Lattices and Miscellanea.- Integral operator with bounded kernel (with Y. Mimura and S. Kakutani) [27].- Quasi-completely-continuous linear functional operations [29].- On the theory of spectra [37].- On regularly convex sets (with M. Fukamiya) [39].- On vector lattice with a unit [40].- Vector lattices and additive set functions [41].- On vector lattice with a unit, II (with M. Fukamiya) [42].- On the representation of the vector lattice [43].- On the semi-ordered ring and its application to the spectral theorem (with T. Nakayama) [44].- On the semi-ordered ring and its application to the spectral theorem, II (with T. Nakayama) [45].- Normed rings and spectral theorems [47].- Normed rings and spectral theorems, II [48].- Normed rings and spectral theorems, III [49].- Normed rings and spectral theorems, IV [50].- Normed rings and spectral theorems, V [51].- Normed rings and spectral theorems, VI [53].- On the representation of functions by Fourier integrals [54].- On the unitary equivalence in general Euclid space [55].- Finitely additive measures (with E. Hewitt) [68].- On the reflexivity of the space of distribution [81].- A note on the fundamental theorem of calculus [104].- V. Semigroups and Evolution Equations.- On the differentiability and the representation of one-parameter semi-group of linear operators [57].- On the differentiability of semi-groups of linear operators [82].- Fractional powers of infinitesimal generators and the analyticity of the semi-groups generated by them [84].- On a class of infinitesimal generators and the integration problem of evolution equations [85].- On the integration of the equation of evolution [88].- Holomorphic semi-groups in a locally convex linear topological space [89].- A perturbation theorem for semi-groups of linear operators [92].- Time dependent evolution equations in a locally convex space [93].- VI. Diffusion Equations.- Integration of Fokker-Planck’s equation in a compact Riemannian space [60].- A theorem of Liouville’s type for meson equation [64].- An ergodic theorem associated with harmonic integrals [65].- Integration of Fokker-Planck’s equation with a boundary condition [66].- Integrability of the backward diffusion equation in a compact Riemannian space [67].- On the existence of the resolvent kernel for elliptic differential operator in a compact Riemann space [70].- On the integration of diffusion equations in Riemannian spaces [71].- On the fundamental solution of the parabolic equation in a Riemannian space [73].- On the integration of the temporally inhomogeneous diffusion equation in a Riemannian space [74].- On the integration of the temporally inhomogeneous diffusion equation in a Riemannian space. II [75].- An abstract analyticity in time for solutions of a diffusion equation [83].- VII. Markov Processes.- An operator-theoretical treatment of temporally homogeneous Markoff process [58].- Brownian motion on the surface of the 3-sphere [59].- An extension of Fokker-Planck’s equation [61].- Stochastic processes built from flows [63].- On Brownian motion in a homogeneous Riemannian space [69].- On the generating parametrix of the stochastic processes [77].- A characterization of the second order elliptic differential operators.- On holomorphic Markov processes [94].- VIII. Hyperbolic Equations.- On Cauchy’s problem in the large for wave equations [72].- An operator-theoretical integration of the wave equation [79].- An operator-theoretical integration of the temporally inhomogeneous wave equation [80].- IX. Potential Theory.- Positive pseudo-resolvents and potentials [91].- Positive resolvents and potentials (An operator-theoretical treatment of Hunt’s theory of potentials) [95].- On the pre-closedness of the potential operator (with T. Watanabe and H. Tanaka) [96].- The existence of the potential operator associated with an equicontinuous semi-group of class (C0) [97].- On the potential operators associated with Brownian motions [98].- On the pre-closedness of Hunt’s potential operators and its applications [99].- On the existence and a characterization of abstract potential operators [100].- Abstract potential operators on Hilbert space [101].- X. Operational Calculus.- A note on Mikusinski’s operational calculus [103].- A note on Mikusinski’s proof of the Titchmarsh convolution theorem (with S. Matsuura) [106].- The algebraic derivative and Laplace’s differential equation [107].- A simple complement to Mikusinski’s operational calculus [108].- Bibliography of Kôsaku Yosida.

O autorze

Kiyosi Itô was born on September 1915, in Kuwana, Japan. After his undergraduate and doctoral studies at Tokyo University, he was associate professor at Nagoya University before joining the faculty of Kyoto University in 1952. He has remained there ever since and is now Professor Emeritus, but has also spent several years at each of Stanford, Aarhus and Cornell Universities and the University of Minnesota. Itô's fundamental contributions to probability theory, especially the creation of stochastic differential and integral calculus and of excursion theory, form a cornerstone of this field. They have led to a profound understanding of the infinitesimal development of Markovian sample paths, and also of applied problems and phenomena associated with the planning, control and optimization of engineering and other random systems.

Blurb

Kôsaku Yosida is world famous as the founder, together with Einar Hille, of the theory of semigroups. These collected papers provide valuable information on how he started and developed functional analysis and operator theoretical methods in the theory of differential equations and probability theory. The book is divided into 10 sections following the main topics on which Yosida worked. Each section includes comments by a specialist of the fields for the benefit of the reader. An extensive bibliography of all Yosida's papers, both English and Japanese, is included. This edition will prove invaluable to anyone wanting a comprehensive view of Yosida's work.