Convergence Theorems

  • György I. Targonski
Conference paper
Part of the Lecture Notes in Mathematics book series (volume 6)


As indicated in Sec. 6 (see (6.19)), the theory of Carleman operators is connected with series of the form
$$ \sum\limits_{{n = 0}}^{\infty } {{a_{n}}} |{\phi _{n}}\left( x \right){|^{2}} $$
where an ≧ {ф and (x)} is some orthonormal system in L2. In fact, a series of this type emerged in the proof of Theorem 9.2 (cf. (9.7)). We shall now investigate the convergence problems of series like (10.1). We first consider two complete orthonormal systems ф and (x) and {ψn (x)} on L2 (a,b), the Hilbert space of complex valued functions of one real variable, defined on the interval [a,b] with -∞ ≤ > b ≤ ∞.


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Copyright information

© Springer-Verlag Berlin · Heidelberg 1967

Authors and Affiliations

  • György I. Targonski
    • 1
  1. 1.Fordham UniversityUSA

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