پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 691 |
| تعداد مقالات | 10,035 |
| تعداد مشاهده مقاله | 71,039,332 |
| تعداد دریافت فایل اصل مقاله | 62,488,789 |
Ergodic properties of pseudo-differential operators on compact Lie groups | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 137، دوره 13، شماره 2، مهر 2022، صفحه 1703-1711 اصل مقاله (395.93 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.25780.3126 | ||
| نویسندگان | ||
| Zahra Faghih؛ Mohammad Bagher Ghaemi* | ||
| School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran | ||
| تاریخ دریافت: 12 دی 1400، تاریخ پذیرش: 22 اسفند 1400 | ||
| چکیده | ||
| Let $ \mathbb{G} $ be a compact Lie group. This article shows that a contraction pseudo-differential operator $ A_{\tau} $ on $ L^{p}(\mathbb{G}) $ has a Dominated Ergodic Estimate (DEE), and is trigonometrically well-bounded. Then we express ergodic generalization of the Vector-Valued M. Riesz theorem for invertible contraction pseudo-differential operator $ A_{\tau} $ on $ L^{p}(\mathbb{G}) $. For this purpose, we show that $ A_{\tau} $ is a Lamperti operator. Then we find a formula for its symbols $ \tau$. According to this formula, a representation for the symbol of adjoint and products is given. | ||
| کلیدواژهها | ||
| Pseudo-differential operators؛ Lamperti operator؛ Dominated Ergodic Estimate؛ trigonometrically well-bounded؛ M. Riesz theorem؛ Adjoints | ||
| مراجع | ||
|
[1] M.A. Akcoglu, A pointwise ergodic theorem in Lp-spaces, Canad. J. Math. 27 (1975), no. 5, 1075–1082. [2] S. Banach, Th´eorie des op´erations lin´eaires, Z. Subwencji funduszu kultury Narodowej, 1979. [3] E. Berkson and T.A. Gillespie, Mean-boundedness and Littlewood-Paley for separation-preserving operators, Trans. Amer. Math. Soc. 349 (1997), no. 3, 1169–1189. [4] R.V. Chacon and U. Krengel, Linear modulus of a linear operator, Proc. Amer. Math. Soc. 15 (1964), no. 4, 553–559. [5] Z. Faghih and M.B. Ghaemi, Characterizations of pseudo-differential operators on S1 based on separationpreserving operators, J. Pseudo-Diff. Oper. Appl. 12 (2021), no. 1, 1–14. [6] M.B. Ghaemi and M. Jamalpour Birgani, Lp-boundedness, compactness of pseudo-differential operators on compact Lie groups, J. Pseudo-Differ. Oper. Appl. 8 (2017), no. 1, 1–11. [7] M.B. Ghaemi, M. Jamalpour Birgani and M.W. Wong, Characterizations of nuclear pseudo-differential operators on S1 with applications to adjoints and products, J. Pseudo-Differ. Oper. Appl. 8 (2017), no. 2, 191–201. [8] M.B. Ghaemi, E. Nabizadeh, M. Jamalpour Birgani and M.K. Kalleji, A study on the adjoint of pseudo-differential operators on compact lie groups, Complex Var. Elliptic Equ. 63 (2018), no. 10, 1408–1420. [9] C.H. Kan, Ergodic properties of Lamperti operators, Canad. J. Math. 30 (1978), no. 6, 1206–1214. [10] J. Lamperti, On the isometries of certain function-spaces, Pacific J. Math. 8 (1958), no. 3, 459–466. [11] W. Rudin, Real and complex analysis, McGraw-Hill Book Company, 1987. [12] M. Ruzhansky and V. Turunen, Pseudo-differential operators and symmetries: Background analysis and advanced topics, Vol. 2. Birkhauser and Boston, 2009. [13] A. Tulcea, Ergodic properties of isometries in Lpspaces 1 < p < ∞, Bull. Amer. Math. Soc. 70 (1964), no. 3,366–371. [14] A. Wolfgang, Spectral properties of Lamperti operators, Indiana Univ. Math. J. 32 (1983), no. 2, 199–215. | ||
|
آمار تعداد مشاهده مقاله: 44,885 تعداد دریافت فایل اصل مقاله: 50,230 |
||