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Các thuộc tính cơ bản của các hàm riêng trong bài toán Sturm–Liouville trên hai khoảng rời nhau
Tóm tắt
Trong bài báo này, chúng tôi xem xét một phương trình Sturm–Liouville cùng với các điều kiện truyền biên phụ thuộc vào tham số riêng trên hai khoảng rời nhau. Chúng tôi xây dựng toán tử giải và hàm Green, đồng thời thu được các công thức xấp xỉ tiệm cận cho các giá trị riêng và các hàm riêng tương ứng. Các kết quả thu được được áp dụng để nghiên cứu các thuộc tính cơ sở của hệ thống các hàm riêng trong không gian Lebesgue $$L_2$$ với các phép đo mới. Cụ thể, chúng tôi chỉ ra rằng chuỗi khai triển hàm riêng liên quan đến hội tụ cư xử theo cách tương tự như chuỗi Fourier thông thường.
Từ khóa
#Sturm–Liouville #hàm riêng #giá trị riêng #điều kiện biên #không gian LebesgueTài liệu tham khảo
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