In this paper, Lorentz space of functions of several variables and Besov＇s class are considered. We establish an exact approximation order of Besov＇s class by partial sums of Fourier＇s series for multiple trigonome...In this paper, Lorentz space of functions of several variables and Besov＇s class are considered. We establish an exact approximation order of Besov＇s class by partial sums of Fourier＇s series for multiple trigonometric system.展开更多
In this paper, we consider a Lorentz space with a mixed norm of periodic functions of many variables. We obtain the exact estimation of the best M-term approximations of Nikol＇skii＇s and Besov＇s classes in the Lore...In this paper, we consider a Lorentz space with a mixed norm of periodic functions of many variables. We obtain the exact estimation of the best M-term approximations of Nikol＇skii＇s and Besov＇s classes in the Lorentz space with the mixed norm.展开更多
A truncated trigonometric, operator-valued moment problem in section 3 of this note is solved. Let be a finite sequence of bounded operators, with arbitrary, acting on a finite dimensional Hilbert space H. A necessary...A truncated trigonometric, operator-valued moment problem in section 3 of this note is solved. Let be a finite sequence of bounded operators, with arbitrary, acting on a finite dimensional Hilbert space H. A necessary and sufficient condition on the positivity of an operator kernel for the existence of an atomic, positive, operator-valued measure , with the property that for every with , the moment of coincides with the term of the sequence, is given. The connection between some positive definite operator-valued kernels and the Riesz-Herglotz integral representation of the analytic on the unit disc, operator-valued functions with positive real part in the class of operators in Section 4 of the note is studied.展开更多
In this work we consider the Von Kármán system with internal damping acting on the displacement of the plate and using the Theorem due to Nakao [1] we prove the exponential decay of the solution.
Let （Zll, . . . , Z1N,... , Zml,. . . , ZmN, Wll,. . . , Wmm） be the coordinates in C^mN＋m2. In this note we prove the analogue of the Theorem of Moser in the case of the real-analytic submanifold M defined as foll...Let （Zll, . . . , Z1N,... , Zml,. . . , ZmN, Wll,. . . , Wmm） be the coordinates in C^mN＋m2. In this note we prove the analogue of the Theorem of Moser in the case of the real-analytic submanifold M defined as follows W=zz-t＋O（3）,where W ={wij}1≤ i,j≤ m and Z ={Zij}1≤i≤ m,1≤j≤N We prove that M is biholomorphically equiva-lent to the model W =zz-tif and only if is formally equivalent to it.展开更多
文摘In this paper, Lorentz space of functions of several variables and Besov＇s class are considered. We establish an exact approximation order of Besov＇s class by partial sums of Fourier＇s series for multiple trigonometric system.
基金supported by the Ministry of Education and Science of Republic Kazakhstan(Grant No.5129/GF4)partially by the Russian Academic Excellence Project(agreement between the Ministry of Education and Science of the Russian Federation and Ural Federal University No.02.A03.21.006 of August 27,2013)
文摘In this paper, we consider a Lorentz space with a mixed norm of periodic functions of many variables. We obtain the exact estimation of the best M-term approximations of Nikol＇skii＇s and Besov＇s classes in the Lorentz space with the mixed norm.
文摘A truncated trigonometric, operator-valued moment problem in section 3 of this note is solved. Let be a finite sequence of bounded operators, with arbitrary, acting on a finite dimensional Hilbert space H. A necessary and sufficient condition on the positivity of an operator kernel for the existence of an atomic, positive, operator-valued measure , with the property that for every with , the moment of coincides with the term of the sequence, is given. The connection between some positive definite operator-valued kernels and the Riesz-Herglotz integral representation of the analytic on the unit disc, operator-valued functions with positive real part in the class of operators in Section 4 of the note is studied.
文摘In this work we consider the Von Kármán system with internal damping acting on the displacement of the plate and using the Theorem due to Nakao [1] we prove the exponential decay of the solution.
文摘Let （Zll, . . . , Z1N,... , Zml,. . . , ZmN, Wll,. . . , Wmm） be the coordinates in C^mN＋m2. In this note we prove the analogue of the Theorem of Moser in the case of the real-analytic submanifold M defined as follows W=zz-t＋O（3）,where W ={wij}1≤ i,j≤ m and Z ={Zij}1≤i≤ m,1≤j≤N We prove that M is biholomorphically equiva-lent to the model W =zz-tif and only if is formally equivalent to it.
