Hirokazu OKAProfessor
■Researcher basic information
Organization
Career
- Apr. 2018, 茨城大学大学院 理工学研究科工学野, 教授
- Apr. 2009, Collegue of Engineering, Ibaraki University, Professor
- Apr. 2007, College of Engineering, Ibaraki University, 准教授
- Apr. 2004, Ibaraki University Faculty of Engineering, Assistant Professor
- Apr. 1996, College of Engineering, Ibaraki University, Lecturer
- Apr. 1993 - Mar. 1995, Department of Mathematics, School of Education, Waseda University, Research Associate
Message from Researchers
(Message from Researchers)
(研究経歴)
Nonlinear ergodic theorems, Volterra integrodifferential equations
■Research activity information
Paper
- Ordered continuous bands on the positive real numbers and distribution
H. Oka; T Miura; N. Niwa and S.-E. Takahasi, Lead
Publ. Math. Debrecen, 08 May 2023, [Reviewed] - Special noncancellative commutative semigroup operations on the real numbers and distribution
T. Miura; N. Niwa; H. Oka and S.-E. Takahasi, Corresponding
Acta Math. Hungar., 22 Dec. 2022, [Reviewed] - Evolution equations governed by quasilinear operators satisfying Caratheodory's conditions
Toshitaka Matsumoto; Hirokazu Oka; Naoki Tanaka
Dissertationes Mathematicae, 02 Feb. 2022, [Reviewed] - A special noncommutative semigroup operation on the real numbers and left or right distribution
Takeshi Miura; Norio Niwa; Hirokazu Oka; Sin-Ei Takahasi, Corresponding
Results in Mathematics, 12 Jan. 2022, [Reviewed] - Semigroup operations which are distributive over a given semigroup operation on positive real numbers
Hirokazu Oka; Takeshi Miura; Sin-Ei Takahasi, Lead, Springer
Acta Scientiarum Mathematicarum (Szeged), 22 Aug. 2020, [Reviewed] - Semigroup operations distributed by natural noncancellative semigroup operations on the positive real numbers
Hirokazu Oka; Takeshi Miura and Sin-Ei Takahasi, Lead, Springer
Semigroup Forum, 09 Aug. 2020, [Reviewed] - Characterization of distributive semigroup operations on the positive real numbers
S.-E. Takahasi; T. Miura and H. Oka, Corresponding, Springer
Semigroup Forum, 22 Mar. 2020, [Reviewed] - 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, [Reviewed] - 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, [Reviewed] - A polynomially spectrum preserving map between uniform algebras.
Go Hirasawa and Hirokazu Oka
Nihonkai Math. J., 2010, [Reviewed] - Stability of almost multiplicative functionals
Norio Niwa; Takeshi Miura; Hirokazu Oka; Sin-Ei Takahasi
Aust. J. Math. Anal. Appl., 04 Sep. 2009, [Reviewed] - 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., Jun. 2009, [Reviewed] - 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, [Reviewed] - A Cauchy-Euler Type Factorization of Operators
Sin-Ei Takahasi; Hirokazu Oka; Takeshi Miura and Hiroyuki Takagi
Tokyo J. Math., Dec. 2008, [Reviewed] - 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, Jul. 2008, [Reviewed] - Ger type stability of the first order linear differential equation y'(t)=h(t)y(t).
Tamsui Oxf. J. Math. Sci., 2008, [Reviewed] - 2-Local Isometries and 2-Local Automorphisms on Uniform Algebras
Osamu Hatori; Takeshi Miura; Hirokazu Oka; Hiroyuki Takagi
International Mathematical Forum, 2007, [Reviewed] - 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, [Reviewed] - An example of multiplicatively spectrum-preserving maps between non-isomorphic semi-simple commutative Banach algebras
Osamu Hatori; Takeshi Miura and Hirokazu Oka, Niigata University
Nihonkai Mathematical Journal, 2007, [Reviewed] - 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, [Reviewed] - 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., Aug. 2005 - 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., Jul. 2003
Books and other publications
Lectures, oral presentations, etc.
Social Contribution Activities
Academic Contribution Activities
