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Caspian Journal of Mathematical Sciences (CJMS)
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Shahriari, M., Jodayree Akbarfam, A. (2023). Inverse problem for Sturm-Liouville operators with a transmission and parameter dependent boundary conditions. Caspian Journal of Mathematical Sciences (CJMS), 6(2), 107-119. doi: 10.22080/cjms.2017.1653
Mohammad Shahriari; Ali Asghar Jodayree Akbarfam. "Inverse problem for Sturm-Liouville operators with a transmission and parameter dependent boundary conditions". Caspian Journal of Mathematical Sciences (CJMS), 6, 2, 2023, 107-119. doi: 10.22080/cjms.2017.1653
Shahriari, M., Jodayree Akbarfam, A. (2023). 'Inverse problem for Sturm-Liouville operators with a transmission and parameter dependent boundary conditions', Caspian Journal of Mathematical Sciences (CJMS), 6(2), pp. 107-119. doi: 10.22080/cjms.2017.1653
Shahriari, M., Jodayree Akbarfam, A. Inverse problem for Sturm-Liouville operators with a transmission and parameter dependent boundary conditions. Caspian Journal of Mathematical Sciences (CJMS), 2023; 6(2): 107-119. doi: 10.22080/cjms.2017.1653

Inverse problem for Sturm-Liouville operators with a transmission and parameter dependent boundary conditions

Article 6, Volume 6, Issue 2, Summer and Autumn 2017, Page 107-119  XML PDF (131 K)
Document Type: Research articles
DOI: 10.22080/cjms.2017.1653
Authors
Mohammad Shahriari; Ali Asghar Jodayree Akbarfam
{Department of Mathematics}, {Faculty of Science}, {University of Maragheh,} {Maragheh-Iran.}
Abstract
In this manuscript, we consider the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. We prove by defining a new Hilbert space and using spectral data of a kind, the potential function can be uniquely determined by a set of value of eigenfunctions at an interior point and part of two sets of eigenvalues.
Keywords
Inverse Sturm--Liouville equation; Non self-adjoint operator; Jump condition; Hilbert space
Article Title [Persian]
مساله وارون برای عملگرهای استورم-لیوویل با شرایط مرزی انتقالی و وابسته به پارامتر
Abstract [Persian]
در این مقاله، مساله معکوس عملگر اشتورم-لیوویل غیرخودالحاق $-D^2+q$ با شرایط مرزی ویژه-پارامتر وابسته و شرایط ناپیوسته در یک بازه متناهی را در نظر می­گیریم. با تعریف فضای هیلبرت جدید و با به کارگیری داده­های طیفی از یک نوع ثابت می­کنیم که تابع پتانسیل می­تواند با معلوم بودن یک مجموعه­ از مقادیر ویژه در یک نقطه درونی و قسمتی از دو مجموعه از مقادیر ویژه تعیین می­شود.
Keywords [Persian]
معادله معکوس اشتورم-لیوویل- عملگر غیر خودالحاق- شرط پرش- فضای هیلبرت
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