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weyl fractional calculus

Proceedings of the Edinburgh Mathematical Society (1)

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ALGEBRA HOMOMORPHISMS FROM REAL WEIGHTED $L^1$ ALGEBRAS
Pedro J. Miana
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 50 / Issue 3 / October 2007

Published online by Cambridge University Press:

08 January 2008, pp. 725-735
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We characterize algebra homomorphisms from the Lebesgue algebra $L^1_\omega(\mathbb{R})$ into a Banach algebra $\mathcal{A}$. As a consequence of this result, every bounded algebra homomorphism $\varPhi:L^1_\omega(\mathbb{R})\to\mathcal{A}$ is approached through a uniformly bounded family of fractional homomorphisms, and the Hille–Yosida theorem for $C_0$-groups is proved.