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Một Giới Hạn Trên Của Độ Dimension Hausdorff Của Tập Phân Kỳ Của Toán Tử Schrödinger Phân Số Trên Hs(ℝn)
Tóm tắt
Cho n ≥ 2 và \(\alpha > \tfrac{1}{2}\), chúng tôi đã đạt được một giới hạn trên cải thiện của độ dimension Hausdorff của toán tử Schrödinger phân số; tức là, \(\mathop {\sup }\limits_{f \in {H^s}({\mathbb{R}^n})} {\dim _H}\left\{ {x \in {{\mathbb{R}^n}}:\;\mathop {\lim }\limits_{t \to 0} {e^{{\rm{i}}t{{( - \Delta )}^\alpha }}}f(x) \ne f(x)} \right\} \le n + 1 - {{2(n + 1)s} \over n}\) cho \(\tfrac{n}{{2(n + 1)}} < s \le \tfrac{n}{2}\).
Từ khóa
Tài liệu tham khảo
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