scholarly journals Approximation of unbounded functionals by the bounded ones in Hilbert space

2012 ◽  
Vol 20 ◽  
pp. 3
Author(s):  
V.F. Babenko ◽  
R.O. Bilichenko
Keyword(s):  
Hilbert Space ◽  
Best Approximation ◽  
Adjoint Operator ◽  
The Best Approximation

We obtained the value of the best approximation of unbounded functional $F_f(x) = (A^kx, f)$ on the class $\{ x\in D(A^r) \colon \| A^r x \| \leqslant 1 \}$ by linear bounded functionals ($A$ is a self-adjoint operator in the Hilbert space $H$, $f\in H$, $k < r$).

scholarly journals The best approximation of classes, defined by powers of self-adjoint operators acting in Hilbert space, by other classes

2021 ◽  
Vol 17 ◽  
pp. 23
Author(s):  
V.F. Babenko ◽  
R.O. Bilichenko
Keyword(s):  
Hilbert Space ◽  
Best Approximation ◽  
Adjoint Operator ◽  
The Best Approximation ◽  
Adjoint Operators

The best approximation of class of elements such that $\| A^k x \| \leqslant 1$ by classes of elements such that $\| A^r x \| \leqslant N$, $N > 0$ for powers $k < r$ of self-adjoint operator $A$ in Hilbert space $H$ is found.

scholarly journals Approximation of unbounded functional, defined by grades of normal operator, on the class of elements of Hilbert space

2016 ◽  
Vol 24 ◽  
pp. 3
Author(s):  
R.O. Bilichenko
Keyword(s):  
Hilbert Space ◽  
Best Approximation ◽  
Normal Operator ◽  
The Best Approximation

We obtain the best approximation of unbounded functional $(A^k x; f)$ on the class $\{ x\in D(A^r) \colon \| A^r x \| \leqslant 1 \}$ by linear bounded functionals for a normal operator $A$ in the Hilbert space $H$ ($k < r$, $f\in H$).

scholarly journals Some problems of approximation theory for powers of normal operators in Hilbert space

2021 ◽  
Vol 18 ◽  
pp. 59
Author(s):  
R.O. Bilichenko
Keyword(s):  
Hilbert Space ◽  
Approximation Theory ◽  
Best Approximation ◽  
Unbounded Operator ◽  
Normal Operator ◽  
The Best Approximation ◽  
Normal Operators

The best approximation of unbounded operator $A^k$ in class with $\| A^r x \| \leqslant 1$ and the best approximation of class with $\|A^k x \| \leqslant 1$ by class with $\| A^r x \| \leqslant N$, $N > 0$ for powers $k < r$ of normal operator $A$ in the Hilbert space $H$ are found.

A note on normal operators

1963 ◽  
Vol 59 (4) ◽  
pp. 727-729 ◽  
Author(s):  
S. J. Bernau ◽  
F. Smithies
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Adjoint Operator ◽  
Spectral Theorem ◽  
Unitary Operators ◽  
Unitary Space ◽  
Bounded Linear ◽  
Finite Dimensional ◽  
Normal Operators ◽  
Finite Dimensional Case

We recall that a bounded linear operator T in a Hilbert space or finite-dimensional unitary space is said to be normal if T commutes with its adjoint operator T*, i.e. TT* = T*T. Most of the proofs given in the literature for the spectral theorem for normal operators, even in the finite-dimensional case, appeal to the corresponding results for Hermitian or unitary operators.

Intracranial volume-pressure relationship in man

1982 ◽  
Vol 56 (4) ◽  
pp. 524-528 ◽  
Author(s):  
Joseph Th. J. Tans ◽  
Dick C. J. Poortvliet
Keyword(s):  
Best Approximation ◽  
Continuous Monitoring ◽  
Fluid Pressure ◽  
Constant Term ◽  
Volume Index ◽  
Intracranial Volume ◽  
Content Type ◽  
The Best Approximation ◽  
Ventricular Fluid Pressure ◽  
Fine Print

✓ The pressure-volume index (PVI) was determined in 40 patients who underwent continuous monitoring of ventricular fluid pressure. The PVI value was calculated using different mathematical models. From the differences between these values, it is concluded that a monoexponential relationship with a constant term provides the best approximation of the PVI.

Constrained best approximation in Hilbert space

1990 ◽  
Vol 6 (1) ◽  
pp. 35-64 ◽  
Author(s):  
Charles K. Chui ◽  
Frank Deutsch ◽  
Joseph D. Ward
Keyword(s):  
Hilbert Space ◽  
Best Approximation ◽  
Constrained Best Approximation
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