• Title/Summary/Keyword: operator.

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SUBORDINATION RESULTS FOR CERTAIN SUBCLASSES BY USING INTEGRAL OPERATOR DEFINED IN THE SPACE OF ANALYTIC FUNCTIONS

  • Sakar, F. Muge;Guney, H. Ozlem
    • Honam Mathematical Journal
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    • v.40 no.2
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    • pp.315-323
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    • 2018
  • In this study, firstly we introduce generalized differential and integral operator, also using integral operator two classes are presented. Furthermore, some subordination results involving the Hadamard product (Convolution) for these subclasses of analytic function are proved. A number of consequences of some of these subordination results are also discussed.

Rank-preserver of Matrices over Chain Semiring

  • Song, Seok-Zun;Kang, Kyung-Tae
    • Kyungpook Mathematical Journal
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    • v.46 no.1
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    • pp.89-96
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    • 2006
  • For a rank-1 matrix A, there is a factorization as $A=ab^t$, the product of two vectors a and b. We characterize the linear operators that preserve rank and some equivalent condition of rank-1 matrices over a chain semiring. We also obtain a linear operator T preserves the rank of rank-1 matrices if and only if it is a form (P, Q, B)-operator with appropriate permutation matrices P and Q, and a matrix B with all nonzero entries.

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INVERSE PROBLEM FOR INTERIOR SPECTRAL DATA OF THE DIRAC OPERATOR

  • Mochizuki, Kiyoshi;Trooshin, Igor
    • Communications of the Korean Mathematical Society
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    • v.16 no.3
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    • pp.437-443
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    • 2001
  • In this paper the inverse problems for the Dirac Operator are studied. A set of values of eigenfunctions in some internal point and spectrum are taken as a data. Uniqueness theorems are obtained. The approach that was used in the investigation of inverse problems for interior spectral data of the Sturm-Liouville operator is employed.

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HYERS-ULAM STABILITY OF A CLOSED OPERATOR IN A HILBERT SPACE

  • Hirasawa Go;Miura Takeshi
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.1
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    • pp.107-117
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    • 2006
  • We give some necessary and sufficient conditions in order that a closed operator in a Hilbert space into another have the Hyers-Ulam stability. Moreover, we prove the existence of the stability constant for a closed operator. We also determine the stability constant in terms of the lower bound.

Hopf Hypersurfaces in Complex Two-plane Grassmannians with Generalized Tanaka-Webster Reeb-parallel Structure Jacobi Operator

  • Kim, Byung Hak;Lee, Hyunjin;Pak, Eunmi
    • Kyungpook Mathematical Journal
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    • v.59 no.3
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    • pp.525-535
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    • 2019
  • In relation to the generalized Tanaka-Webster connection, we consider a new notion of parallel structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians and prove the non-existence of real hypersurfaces in $G_2({\mathbb{C}}^{m+2})$ with generalized Tanaka-Webster parallel structure Jacobi operator.

ON SPECTRAL CONTINUITIES AND TENSOR PRODUCTS OF OPERATORS

  • Kim, In Hyoun
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.1
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    • pp.113-119
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    • 2011
  • Let T be a bounded linear operator on a complex Hilbert space $\mathcal{H}$. An operator T is called class A operator if ${\left|{T^2}\right|}{\geq}{\left|{T^2}\right|}$ and is called class A(k) operator if $({T^*\left|T\right|^{2k}T})^{\frac{1}{k+1}}{\geq}{\left|T\right|}^2$. In this paper, we show that ${\sigma}$ is continuous when restricted to the set of class A operators and consider the tensor products of class A(k) operators.

ABSOLUTE CONTINUITY OF THE MAGNETIC SCHRÖDINGER OPERATOR WITH PERIODIC POTENTIAL

  • Assel, Rachid
    • Korean Journal of Mathematics
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    • v.26 no.4
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    • pp.601-614
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    • 2018
  • We consider the magnetic $Schr{\ddot{o}}dinger$ operator coupled with two different potentials. One of them is a harmonic oscillator and the other is a periodic potential. We give some periodic potential classes for which the operator has purely absolutely continuous spectrum. We also prove that for strong magnetic field or large coupling constant, there are open gaps in the spectrum and we give a lower bound on their number.