Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

CONTENTSIntroductionChapter I. Non-harmonic Fourier series (behaviour on the initial interval) ??1.1. Minimal systems of exponentials ??1.2. Expansions of functions in , ??1.3. Expansions of functions in Comments and supplements Chapter II. Non-harmonic Fourier series (the behaviour on the real axis) ??2.1. Extension of convergence of quasi-polynomials ??2.2. Continuation of functions from the initial interval ??2.3. Convergence and summability of non-harmonic Fourier series in the -norm () on every segmentComments and supplements Chapter III. Properties of the system ??3.1. Basis properties ??3.2. Angles between subspaces of exponentials Comments and supplements References

http://iopscience.iop.org/article/10.1070/RM1982v037n05ABEH004044/pdf

Biorthogonal expansions of functions in series of exponents on intervals of the real axis

We prove that in the class of separated sequences there exists a sequence whose real parts decrease arbitrarily slowly to , so that for some continuous function on the general term of the nonharmonic Fourier series diverges to infinity as for all .

http://iopscience.iop.org/article/10.1070/IM1995v045n03ABEH001673/pdf

Nonharmonic fourier series without the riemann-lebesgue property

We consider a biorthogonal expansion in terms of the system , where are the zeros of the entire function and has bounded variation for some integer , for , and . The function to be expanded has domain . We describe the sets of convergence (and divergence) of the series for the classes , , , and . The results indicate that the series have properties different from those of ordinary Fourier series; and the difference becomes more pronounced as increases.Bibliography: 16 titles.

http://iopscience.iop.org/0025-5726/11/2/A10/pdf/0025-5726_11_2_A10.pdf

A M Sedleckiĭ

Papers

On a class of biorthogonal expansions in exponential functions