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arXiv · 2405.15814

Spectral theory for fractal pseudodifferential operators

Hans Triebel
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Abstract

The paper deals with the distribution of eigenvalues of the compact fractal pseudodifferential operator $T^\mu_\tau$, \[ \big( T^\mu_\tau f\big)(x) = \int_{\mathbb{R}^n} e^{-ix\xi} \, \tau(x,\xi) \, \big( f\mu \big)^\vee (\xi) \, \mathrm{d} \xi, \qquad x\in \mathbb{R}^n, \] in suitable special Besov spaces $B^s_p (\mathbb{R}^n) = B^s_{p,p} (\mathbb{R}^n)$, $s>0$, $1 0, \quad 1<p<\infty. \] We add at the end of the paper a few personal reminiscences illuminating the role of Pietsch in connection with the creation of approximation numbers and entropy numbers.

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Hans Triebel. 2024-05-22. Spectral theory for fractal pseudodifferential operators. https://arxiv.org/abs/2405.15814

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