Collected Papers

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.