Cosine families, invariant subspaces, and boundary conditions for a class of diffusions on star graphs
Artykuł w czasopiśmie
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brak dyscyplin
| Status: | |
| Autorzy: | Ratajczyk Elżbieta |
| Dyscypliny: | |
| Aby zobaczyć szczegóły należy się zalogować. | |
| Rok wydania: | 2026 |
| Wersja dokumentu: | Drukowana | Elektroniczna |
| Język: | angielski |
| Wolumen/Tom: | 289 |
| Strony: | 33 - 52 |
| Impact Factor: | 0,7 |
| Web of Science® Times Cited: | 0 |
| Scopus® Cytowania: | 0 |
| Bazy: | Web of Science | Scopus |
| Efekt badań statutowych | NIE |
| Materiał konferencyjny: | NIE |
| Publikacja OA: | NIE |
| Abstrakty: | angielski |
| This paper explores the interplay between boundary conditions and invariant subspaces for one-dimensional Laplacians, extending these concepts to Walsh’s spider process on a star-like graph. We establish a precise correspondence between the transmission condition characterizing this process and a specific subspace within a larger function space. This correspondence is facilitated by relating the cosine family associated with the spider process to the basic cosine family of unrestricted Brownian motion. Furthermore, we introduce a complementary subspace, leading to a novel decomposition of the function space that generalizes known results for simpler boundary conditions. This decomposition reveals a fundamental relationship between two distinct transmission conditions, highlighting their complementary nature. Our findings provide new insights into the structure of Walsh’s spider process and offer a framework for further analysis, including the study of its limiting behavior as the stickiness parameter varies. |
