On the Riccati equations

@article{Karaev2008OnTR,
  title={On the Riccati equations},
  author={Mubariz T. Karaev},
  journal={Monatshefte f{\"u}r Mathematik},
  year={2008},
  volume={155},
  pages={161-166}
}
  • M. Karaev
  • Published 21 May 2008
  • Mathematics
  • Monatshefte für Mathematik
Abstract.In this article we give, in terms of so-called Berezin symbols, some necessary conditions for the solvability of the Riccati equation $$XAX+XB-CX-D=0$$ on the set ${\cal T}$ of all Toeplitz operators on the Hardy space $H^2({\Bbb D})$. 
View on Springer
faculty.ksu.edu.sa
30 Citations
Background Citations
9
Methods Citations
4

30 Citations

Riccati equations and Toeplitz-Berezin type symbols on Dirichlet space of unit ball

The present paper mainly gives some applications of Berezin type symbols on the Dirichlet space of unit ball. We study the solvability of some Riccati operator equations of the form XAX + XB - CX = D…

Riccati equations and Toeplitz-Berezin type symbols on Dirichlet space of unit ball

The present paper mainly gives some applications of Berezin type symbols on the Dirichlet space of unit ball. We study the solvability of some Riccati operator equations of the form XAX + XB - CX = D…

Some results for operators on a model space

We investigate some problems for truncated Toeplitz operators. Namely, the solvability of the Riccati operator equation on the set of all truncated Toeplitz operators on the model space Kθ = H2ΘθH2…

Some results for operators on a model space

We investigate some problems for truncated Toeplitz operators. Namely, the solvability of the Riccati operator equation on the set of all truncated Toeplitz operators on the model space Kθ = H2ΘθH2…

Remarks on the zero Toeplitz product problem in the Bergman and Hardy spaces

In this article, we are interested in the zero Toeplitz product problem: for two symbols f, g ∈ L∞ (D, dA) , if the product TfTg is identically zero on L 2 a (D) , then can we claim Tf or Tg is…

Properties of solutions of matrix Riccati

. In this paper we study properties of regular solutions of matrix Riccati equations. The obtained results are used to study the asymptotic behavior of solutions of linear systems of ordinary…

Properties of solutions of quaternionic Riccati equations

. In this paper we study properties of regular solutions of quaternionic Riccati equations. The obtained results we use for study of the asymptotic behavior of solutions of two first-order linear…

Regularity of Normal Forms on Parameters

For nonautonomous differential equations depending on a parameter, we show that the normal form inherits the regularity on the parameter of the original equation, provided that the nonresonances…

Use of reproducing kernels and Berezin symbols technique in some questions of operator theory

Abstract. We give in terms of Berezin symbols some characterizations for the operators belonging to the Schatten–von Neumann classes , , which were motivated by the questions posed by Nordgren and…

On the Berezin Symbols and Toeplitz Operators

The present paper mainly gives some new applications of Berezin symbols. In particular, the Berezin symbol is used in approximation problem for H1-functions. We study also asymptotic multiplicativity…

References

SHOWING 1-10 OF 18 REFERENCES

Existence and Uniqueness of Contractive Solutions of Some Riccati Equations

Abstract In this paper we establish criteria for the existence and uniqueness of contractive solutions K of the Riccati equation KBK + KA − DK − C =0 under the assumption that the spectra of A and D…

Berezin Symbols and Schatten--von Neumann Classes

AbstractIn terms of Berezin symbols, we give several criteria for operators to belong to the Schatten--von Neumann classes $$\mathfrak{S}_p $$ . In particular, for functions of model operators, we…

The Berezin transform and radial operators

We analyze the connection between compactness of operators on the Bergman space and the boundary behaviour of the corresponding Berezin transform. We prove that for a special class of operators that…

Invariant subspaces of Toeplitz operators

This paper is devoted to the problem of the existence of invariant subspaces for Toeplitz operators. Let Γ be a Lipschitzian arc in the plane and let f be a non-constant continuous functions on the…

On some problems related to Berezin symbols

Toeplltz operators and the Berezin transform on H2

A new concept for block operator matrices:the quadratic numerical range

Analysis and modificaton of Newton's method for algebraic Riccati equations

It is found that a simple modification can improve the performance of the Newton iteration dramatically and the convergence is quadratic if the Frechet derivative is invertible at the solution.

SPECTRUM, SIMILARITY, AND INVARIANT SUBSPACES OF TOEPLITZ OPERATORS

Estimates are obtained for the resolvents of Toeplitz operators under certain restrictions on their symbols. Conditions are found for the existence of nontrivial invariant subspaces and for a…

Operator theory in function spaces

Bounded linear operators Interpolation of Banach spaces Integral operators on $L^p$ spaces Bergman spaces Bloch and Besov spaces The Berezin transform Toeplitz operators on the Bergman space Hankel…