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Yapay Zeka Hızlı Bakış & Çıkarımlar
AI Insight⚡ TL;DR(1 Cümlede Hızlı Çıkarım)
We also prove the Parseval equality and thespectral expansion formula in terms of the spectral function for this system on the whole line.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:We consider the singular Hahn–Dirac system defined by$-frac1qD_{-wq^{-1},q^{-1}}y_2+p(x)y_1=lambda y_1$$D_{w,q}y_1+r(x)y_2=lambda y_2$where $lambda$ is a complex spectral parameter and p and r are real-valued functions defined on $(-infty,infty)$ and continuousat $omega_0$ .
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Temel Bulgular & Veri:We prove the existence of a spectral function for such a system.
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Sonuç & Katkı:We also prove the Parseval equality and thespectral expansion formula in terms of the spectral function for this system on the whole line.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri
Abstract
We consider the singular Hahn–Dirac system defined by$-frac1qD_{-wq^{-1},q^{-1}}y_2+p(x)y_1=lambda y_1$$D_{w,q}y_1+r(x)y_2=lambda y_2$where $lambda$ is a complex spectral parameter and p and r are real-valued functions defined on $(-infty,infty)$ and continuousat $omega_0$ . We prove the existence of a spectral function for such a system. We also prove the Parseval equality and thespectral expansion formula in terms of the spectral function for this system on the whole line.
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Bu Makaleye Atıf Yap
ALLAHVERDIEV, B. P., TUNA, H. (2022). The spectral expansion for the Hahn–Dirac system on the whole line. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 3, 1668–1687. https://ajindex.com/articles/607985