Eigensubspaces and Fourier Transform
Lev Sakhnovich · Birkhäuser Basel eBooks · 1996
In the space L p (0, ω) (1 ≤ p ≤ 2) let a bounded operator be given of the form 0.1 $$Sf = \frac{d}{{dx}}\int\limits_0^\omega {s\left( {x - t} \right)} f\left( t \right)dt, s\left( x \right) \in {L^q}\left( { - \omega ,\omega } \right)$$ where $$\frac{1}{p} + \frac{1}{q} = 1$$ . We denote by H v a collection of solutions of the equation 0.2 $$Sf = vf, f \in {L^p}\left( {0,\omega } \right)$$