In the early 1920s, he worked on the moment problem, to which he introduced the operator-theoretic approach by proving the Riesz extension theorem ( which predated the closely related Hahn & ndash; Banach theorem ).
22.
The uniqueness of " & mu; " in the Hausdorff moment problem follows from the Weierstrass approximation theorem, which states that polynomials are dense under the uniform norm in the space of continuous functions on [ 0, 1 ].
23.
The Stieltjes moment problems and the Hamburger moment problems, if they are solvable, may have infinitely many solutions ( indeterminate moment problem ) whereas a Hausdorff moment problem always has a unique solution if it is solvable ( determinate moment problem ).
24.
The Stieltjes moment problems and the Hamburger moment problems, if they are solvable, may have infinitely many solutions ( indeterminate moment problem ) whereas a Hausdorff moment problem always has a unique solution if it is solvable ( determinate moment problem ).
25.
The Stieltjes moment problems and the Hamburger moment problems, if they are solvable, may have infinitely many solutions ( indeterminate moment problem ) whereas a Hausdorff moment problem always has a unique solution if it is solvable ( determinate moment problem ).
26.
The Stieltjes moment problems and the Hamburger moment problems, if they are solvable, may have infinitely many solutions ( indeterminate moment problem ) whereas a Hausdorff moment problem always has a unique solution if it is solvable ( determinate moment problem ).
27.
The Stieltjes moment problems and the Hamburger moment problems, if they are solvable, may have infinitely many solutions ( indeterminate moment problem ) whereas a Hausdorff moment problem always has a unique solution if it is solvable ( determinate moment problem ).
28.
I should think a little to give you a precise derivation for your CF this way, but as you are interested in the topic, you can have a look to Akhiezer's book on the classical moment problem, where everything is very clearly explained.
29.
In " Moment problems for a finite interval " of 1923 he treated more special moment problems, such as those with certain restrictions for generating density \ varphi ( x ), for instance \ varphi ( x ) \ in L ^ p [ 0, 1 ].
30.
In " Moment problems for a finite interval " of 1923 he treated more special moment problems, such as those with certain restrictions for generating density \ varphi ( x ), for instance \ varphi ( x ) \ in L ^ p [ 0, 1 ].
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