- PII
- 10.31857/S2686954323600568-1
- DOI
- 10.31857/S2686954323600568
- Publication type
- Status
- Published
- Authors
- Volume/ Edition
- Volume 514 / Issue number 1
- Pages
- 79-81
- Abstract
- In this paper, we construct a strongly continuous operator group generated by a one-dimensional Dirac operator acting in the space \(\mathbb{H} = {{\left( {{{L}_{2}}[0,\pi ]} \right)}^{2}}\). The potential is assumed to be summable. It is proved that this group is well-defined in the space \(\mathbb{H}\) and in the Sobolev spaces \(\mathbb{H}_{U}^{\theta }\), \(\theta > 0\), with fractional index of smoothness \(\theta \) and under boundary conditions \(U\). Similar results are proved in the spaces \({{\left( {{{L}_{\mu }}[0,\pi ]} \right)}^{2}}\), \(\mu \in (1,\infty )\). In addition we obtain estimates for the growth of the group as \(t \to \infty \).
- Keywords
- оператор Дирака суммируемый потенциал операторная группа
- Date of publication
- 01.01.2023
- Year of publication
- 2023
- Number of purchasers
- 0
- Views
- 48
References
- 1. Шкаликов А.А. // УМН. 1979. Т. 34. № 5(209). С. 235–236.
- 2. Savchuk A.M., Shkalikov A.A. // Math. Notes. 2014. V. 96 № 5. P. 777–810.
- 3. Гомилко А.M. // Функц. анализ и его прил. 1999. Т. 33 № 4. С. 66–69.
- 4. Albeverio S., Hryniv R., Mykytyuk Ya. // Russian J. Math. Phys. 2005. V. 12. № 4. P. 406–42.
- 5. Баскаков А.Г., Дербушев А.В., Щербаков А.О. // Изв. РАН. Сер. матем. 2011. Т. 75. № 3. С. 3–28.
- 6. Djakov P., Mityagin B. // Proc. Amer. Math. Soc. 2013. V. 141. № 4. P. 1361–1375.
- 7. Beigl A., Eckhardt J., Kostenko A., Teschl G. // J. Math. Phys. 2015. V. 56, 012102.
- 8. Djakov P., Mityagin B. // Russ. Math. Surv. 2020. V. 75. № 4. P. 587–626.
- 9. Савчук А.М., Садовничая И.В. // Совр. мат-ка. Фунд. напр-я. 2020. Т. 66. № 3. С. 373–530.
- 10. Лунев А.А., Маламуд М.М. // Зап. научн. сем. ПОМ-И. 2022. Т. 516. С. 69–120.
