Ingham type theorems and applications to control theory

Claudio Baiocchi; Vilmos Komornik; Paola Loreti

Displaying similar documents to “Ingham type theorems and applications to control theory”

Oscillations of anharmonic Fourier series and the wave equation.

Alain Haraux, Vilmos Komornik (1985)

Revista Matemática Iberoamericana

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In this paper we have collected some partial results on the sign of u(t,x) where u is a (sufficiently regular) solution of ⎧ u_tt + (-1)^m Δ^mu = 0 (t,x) ∈ R x Ω ⎨ ⎩ u_|Γ = ... = Δ^m-1 u_|Γ = 0 t ∈ R. These results rely on the study of a sign of almost periodic functions of a special...

On an infinite linear combination of partial sums of Fourier series

Rajendra Sinha (1976)

Studia Mathematica

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Integrability theorems for trigonometric series

Bruce Aubertin, John Fournier (1993)

Studia Mathematica

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We show that, if the coefficients (an) in a series $a_{0} / 2 + \sum_{n = 1}^{\infty} a_{n} c o s (n t)$ tend to 0 as n → ∞ and satisfy the regularity condition that $\sum_{m = 0}^{\infty} {\sum_{j = 1}^{\infty} [\sum_{n = j 2^{m}}^{(j + 1) 2^{m} - 1} | a_{n} - a_{n + 1} |] ²}^{1 / 2} < \infty$ , then the cosine series represents an integrable function on the interval [-π,π]. We also show that, if the coefficients (bn) in a series $\sum_{n = 1}^{\infty} b_{n} s i n (n t)$ tend to 0 and satisfy the corresponding regularity condition, then the sine series represents an integrable function on [-π,π] if and only if $\sum_{n = 1}^{\infty} | b_{n} | / n < \infty$ . These conclusions were previously known to hold under stronger restrictions on the sizes...

On the Fourier coefficients of a simple discontinuous function

Fu Cheng Hsiang (1967)

Compositio Mathematica

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Absolute convergence of Fourier series of a function of Wiener’s class $V_{p}$

Siddiqi, Rafat N. (1979)

Portugaliae mathematica

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Almost everywhere convergence of Walsh Fourier series of $H^{1}$ -functions

N. Ladhawala, D. Pankratz (1976)

Studia Mathematica

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The converse of Wiener-Levy-Marcinkiewicz theorem

N. Riviere, Y. Sagher (1966)

Studia Mathematica

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On the theorem of Ivasev-Musatov. II

Thomas-William Korner (1978)

Annales de l'institut Fourier

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As in Part I [Annales de l’Inst. Fourier, 27-3 (1997), 97-113], our object is to construct a measure whose support has Lebesgue measure zero, but whose Fourier transform drops away extremely fast.