オカ ヒロカズ岡 裕和教授Hirokazu OKA
■研究者基本情報
経歴
研究者からのメッセージ
(研究者からのメッセージ)
(研究経歴)
非線形エルゴード定理, Volterra 積分微分方程式
■研究活動情報
論文
- Ordered continuous bands on the positive real numbers and distribution
H. Oka; T Miura; N. Niwa and S.-E. Takahasi, 筆頭著者
Publ. Math. Debrecen, 2023年05月08日, ［査読有り］ - Special noncancellative commutative semigroup operations on the real numbers and distribution
T. Miura; N. Niwa; H. Oka and S.-E. Takahasi, 責任著者
Acta Math. Hungar., 2022年12月22日, ［査読有り］ - Evolution equations governed by quasilinear operators satisfying Caratheodory's conditions
Toshitaka Matsumoto; Hirokazu Oka; Naoki Tanaka
Dissertationes Mathematicae, 2022年02月02日, ［査読有り］ - A special noncommutative semigroup operation on the real numbers and left or right distribution
Takeshi Miura; Norio Niwa; Hirokazu Oka; Sin-Ei Takahasi, 責任著者
Results in Mathematics, 2022年01月12日, ［査読有り］ - Semigroup operations which are distributive over a given semigroup operation on positive real numbers
Hirokazu Oka; Takeshi Miura; Sin-Ei Takahasi, 筆頭著者, Springer
Acta Scientiarum Mathematicarum (Szeged), 2020年08月22日, ［査読有り］ - Semigroup operations distributed by natural noncancellative semigroup operations on the positive real numbers
Hirokazu Oka; Takeshi Miura; Sin-Ei Takahasi, 筆頭著者, Springer
Semigroup Forum, 2020年08月09日, ［査読有り］ - Characterization of distributive semigroup operations on the positive real numbers
S.-E. Takahasi; T. Miura; H. Oka, 責任著者, Springer
Semigroup Forum, 2020年03月22日, ［査読有り］ - Semigroup operations distributed by the ordinary multiplication or addition on the real numbers
Sin-Ei Takahasi; Hiroyuki Takagi; Takeshi Miura; Hirokazu Oka, We characterize the cancellative and continuous semigroup operations on the real field which are distributed by the ordinary multiplication or addition., KOSSUTH LAJOS TUDOMANYEGYETEM
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2017年, ［査読有り］ - Global solvability for abstract semilinear evolution equations.
Hirokazu Oka and Naoki Tanaka, The Cauchy problem for the abstract semilinear evolution equation u'(t) = Au(t) + B(u(t)) + C(u(t)) is discussed in a general Banach space X. Here A is the so-called Hille-Yosida operator in X, B is a differentiable operator from D(A) into X, and C is a locally Lipschitz continuous operator from D(A) into itself. A vector-valued functional defined only on X is used and appropriate conditions on the nonlinear operators B and C are imposed so that a vector-valued functional defined on the domain of the operator A may be constructed in order to specify the growth of a global solution. The advantage of our formulation lies in the fact that it is possible to obtain a global solution by checking some energy inequalities concerning only low order derivatives. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, WILEY-V C H VERLAG GMBH
Math. Nachr., 2010年, ［査読有り］ - A polynomially spectrum preserving map between uniform algebras.
Go Hirasawa; Hirokazu Oka
Nihonkai Math. J., 2010年, ［査読有り］ - Stability of almost multiplicative functionals
N.Niwa; T.Miura; H.Oka; Sin-Ei Takahasi
Aust. J. Math. Anal. Appl., 2009年09月04日, ［査読有り］ - Peripheral multiplicativity of maps on uniformly closed algebras of continuous functions which vanish at infinity
O.Hatori; T.Miura; H.Oka; H.Takagi, We study maps between uniformly closed algebras of complex-valued continuous functions which vanish at infinity on locally compact Hausdorff spaces. Without assuming linearity nor multiplicativity on the maps we show that they are isometrical isomorphisms as Banach space operators if they satisfy that the peripheral range of the product of the images of any two elements coincides with the peripheral range of the product of those elements. Furthermore, if the underlying algebras contain approximate identities, then they are isometrically isomorphic as Banach algebras, which is a generalization of a recent result of Luttman and Tonev for the case of uniform algebras. On the other hand it is not the case without assuming the existence of approximate identities
An example is given. © 2009 International Academic Printing Co. Ltd. All rights reserved.
Tokyo J. Math., 2009年06月, ［査読有り］ - Peripherally Monomial-Preserving Maps between Uniform Algebras
Osamu Hatori; Kazumi Hino; Takeshi Miura; Hirokazu Oka, Let A and B be uniform algebras and p(z, w) = z(m)w(n) a two-variable monomial. We characterize maps T from certain subsets of A into B such that sigma(pi)(p(T(f), T(g))) subset of sigma(pi)(p(f, g)) holds for all f and g in the domain of T; peripherally monomial-preserving maps. Furthermore A and B are proved to be isometrical isomorphic as Banach algebras. If the greatest common divisor of m and n is 1, then T is extended to an isometrical linear isomorphism; a weighted composition operator. An example of peripherally monomial-preserving surjections between uniform algebras which is not linear, nor multiplicative, nor injective is given when the greatest common divisor is strictly greater than 1., SPRINGER BASEL AG
Mediterr. J. Math., 2009年, ［査読有り］ - A Cauchy-Euler Type Factorization of Operators
Sin-Ei Takahasi; Hirokazu Oka; Takeshi Miura; Hiroyuki Takagi
Tokyo J. Math., 2008年12月, ［査読有り］ - On surjective ring homomorphisms between semi-simple,commutative Banach algebras
Takeshi Miura; Sin-Ei Takahasi; Norio Niwa and Hirokazu Oka, Let A and B be semi-simple commutative Banach algebras. We give a, representation of surjective ring homomorphisms from A onto B in terms of complex ring homomorphisms and injective, continuous and closed mapping between the maximal ideal spaces. As a corollary, we prove that neither the disc algebra A((D) over bar) nor the commutative Banach algebra of all bounded holomorphic functions H-infinity(D) are ring homomorphic image of any semi-simple commutative regular Banach algebras. Under additional assumptions on the maximal ideal spaces, we also prove automatic linearity of ring homomorphisms., KOSSUTH LAJOS TUDOMANYEGYETEM
Publ. Math. Debrecen, 2008年07月, ［査読有り］ - Ger type stability of the first order linear differential equation y'(t)=h(t)y(t).
Tamsui Oxf. J. Math. Sci., 2008年, ［査読有り］ - 2-Local Isometries and 2-Local Automorphisms on Uniform Algebras
Osamu Hatori; Takeshi Miura; Hirokazu Oka; Hiroyuki Takagi
International Mathematical Forum, 2007年, ［査読有り］ - Superstability of multipliers and ring derivations on Banach algebras
Takeshi Miura; Hirokazu; Oka; Go; Hirasawa; Sin-Ei Takahasi, In this paper, we will consider Hyers-Ulam-Rassias stability of multipliers and ring derivations between Banach algebras. As a corollary, we will prove superstability of ring derivations and multipliers. That is, approximate multipliers and approximate ring derivations are exact multipliers and ring derivations., BANACH MATHEMATICAL RESEARCH GROUP
Banach J. Math. Anal., 2007年, ［査読有り］ - An example of multiplicatively spectrum-preserving maps between non-isomorphic semi-simple commutative Banach algebras
Osamu Hatori; Takeshi Miura; Hirokazu Oka, 新潟大学
Nihonkai Mathematical Journal, 2007年, ［査読有り］ - Hyers-Ulam stability of the first order linear differential equation for Banach space-valued holomorphic mappings
Takeshi Miura; Hirokazu Oka; Sin-Ei Takahasi; Norio Niwa
J. Math. Inequal., 2007年, ［査読有り］ - Evolution operators genereted by non-densely defined operators
Hirokazu Oka; Naoki Tanaka, In this paper it is shown that an evolution operator is generated by a family of closed linear operators whose common domain is not necessarily dense in the underlying Banach space, under the stability condition proposed by the second author from the viewpoint of finite difference approximations. (c) 2005 WILEY-VCH Verlag GmbH & Co. KG&A, Weinheim., WILEY-V C H VERLAG GMBH
Math. Nachr., 2005年08月 - On the structure of the solution set of a third kind boundary value problem
Sin-ei Takahasi; Hirokazu Oka; Takeshi Miura, We show that given any closed subset C of a real Banach space E, there is a continuous function f(t, x) which is Lipschitz continuous in its second variable such that the solution set of the corresponding third kind boundary value problem is homeomorphic to C (Theorem 1.1). In the special problem we give the infimum of Lipschitz constants L-f of such functions f (t, x) (Theorem 1.3)., WILEY-V C H VERLAG GMBH
Math. Nachr., 2003年07月
書籍等出版物
講演・口頭発表等
- Carath\'eodory条件を満たす準線形作用素に支配される発展方程式に対する適切性と近似可解性について
2020日本数学会・秋季総合分科会, 2020年09月25日
20200922, 20200925 - 正数空間上の半群演算と分配法則
髙橋眞映 (山形大学名誉教授)
RIMS 共同研究 (公開型) 関数空間の一般化とその周辺, 2018年11月26日, 研究代表者 松岡勝男(日本大学経済学部), ［招待有り］ - 掛け算や足し算によって分配される実数上のある種の半群演算の決定
髙橋眞映; 高木啓行; 三浦 毅; 岡 裕和
2018年度日本数学会年会 函数解析学分科会, 2018年03月19日, 日本数学会
社会貢献活動
学術貢献活動
