Criticality transition for positive powers of the discrete Laplacian on the half line
Gerhát BM, Krejčiřík D, Štampach F. 2025. Criticality transition for positive powers of the discrete Laplacian on the half line. Revista Matematica Iberoamericana. 41(3), 1173–1200.
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Author
Gerhát, Borbála MISTA;
Krejčiřík, David;
Štampach, František
Corresponding author has ISTA affiliation
Department
Abstract
We study the criticality and subcriticality of powers (−Δ) α with α>0 of the discrete Laplacian −Δ acting on ℓ 2 (N). We prove that these positive powers of the Laplacian are critical if and only if α≥3/2. We complement our analysis with Hardy-type inequalities for (−Δ) α in the subcritical regimes α∈(0,3/2). As an illustration of the critical case α≥3/2, we analyze asymptotic properties of discrete eigenvalues emerging by coupling (−Δ) α with a localized potential.
Publishing Year
Date Published
2025-01-23
Journal Title
Revista Matematica Iberoamericana
Publisher
EMS Press
Acknowledgement
We are grateful to Petr Siegl for a helpful suggestion leading to Hardy weights with the expected optimal decay rate.
The authors acknowledge the support of the EXPRO grant no. 20-17749X of the Czech Science Foundation.
Volume
41
Issue
3
Page
1173-1200
ISSN
eISSN
IST-REx-ID
Cite this
Gerhát BM, Krejčiřík D, Štampach F. Criticality transition for positive powers of the discrete Laplacian on the half line. Revista Matematica Iberoamericana. 2025;41(3):1173-1200. doi:10.4171/RMI/1523
Gerhát, B. M., Krejčiřík, D., & Štampach, F. (2025). Criticality transition for positive powers of the discrete Laplacian on the half line. Revista Matematica Iberoamericana. EMS Press. https://doi.org/10.4171/RMI/1523
Gerhát, Borbála M, David Krejčiřík, and František Štampach. “Criticality Transition for Positive Powers of the Discrete Laplacian on the Half Line.” Revista Matematica Iberoamericana. EMS Press, 2025. https://doi.org/10.4171/RMI/1523.
B. M. Gerhát, D. Krejčiřík, and F. Štampach, “Criticality transition for positive powers of the discrete Laplacian on the half line,” Revista Matematica Iberoamericana, vol. 41, no. 3. EMS Press, pp. 1173–1200, 2025.
Gerhát BM, Krejčiřík D, Štampach F. 2025. Criticality transition for positive powers of the discrete Laplacian on the half line. Revista Matematica Iberoamericana. 41(3), 1173–1200.
Gerhát, Borbála M., et al. “Criticality Transition for Positive Powers of the Discrete Laplacian on the Half Line.” Revista Matematica Iberoamericana, vol. 41, no. 3, EMS Press, 2025, pp. 1173–200, doi:10.4171/RMI/1523.
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