• DOI:10.1186/s13662-020-03206-7
• Corpus ID: 230988430

Fundamental solutions for semidiscrete evolution equations via Banach algebras

@article{GonzlezCamus2021FundamentalSF,
  title={Fundamental solutions for semidiscrete evolution equations via Banach algebras},
  author={Jorge Gonz{\'a}lez-Camus and Carlos Lizama and Pedro J. Miana},
  journal={Advances in Difference Equations},
  year={2021},
  volume={2021}
}

• Jorge González-Camus, C. Lizama, Pedro J. Miana
• Published 7 January 2021
• Mathematics
• Advances in Difference Equations

We give representations for solutions of time-fractional differential equations that involve operators on Lebesgue spaces of sequences defined by discrete convolutions involving kernels through the discrete Fourier transform. We consider finite difference operators of first and second orders, which are generators of uniformly continuous semigroups and cosine functions. We present the linear and algebraic structures (in particular, factorization properties) and their norms and spectra in the Lebesgue space of summable sequences. We identify fractional powers of these generators and apply to them the subordination principle. We also give some applications and consequences of our results.