Tamarkin's work spanned a number of areas, including number theory, integral equations, Fourier series, complex analysis, moment problem, boundary value problem and differential equations.
12.
For a bounded interval, the collection of all the moments ( of all orders, from to ) uniquely determines the distribution ( Hausdorff moment problem ).
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So in this case the solution to the Hamburger moment problem is unique and " ? ", being the spectral measure of " T ", has finite support.
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An important variation is the truncated moment problem, which studies the properties of measures with fixed first " k " moments ( for a finite " k " ).
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In the late 19th century, the study of continued fractions to solve the moment problem by T . J . Stieltjes led to the general notion of orthogonal polynomials.
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The moment problem for the Stieltjes Wigert polynomials is indeterminate; in other words, there are many other measures giving the same family of orthogonal polynomials ( see Krein's condition ).
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A month later in September, a new boson was proposed by Yu-Sheng, McKeen and Miller to resolve both the proton radius puzzle and the muon's anomalous magnetic dipole moment problem.
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The set of polynomials may or may not be dense in the associated Hilbert spaces if the moment problem is indeterminate, and it depends on whether measure is extremal or not.
19.
Every Hausdorff method is given by a moment sequence; in this context Hausdorff gave an elegant solution of the moment problem for a finite interval, bypassing the theory of continued fractions.
20.
The Hamburger moment problem is solvable ( that is, { " m n " } is a sequence of moments ) if and only if the corresponding Hankel kernel on the nonnegative integers
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