There are three basic types of self-adjoint regular and singular boundary conditions: separated, coupled, and mixed. For even order problems with real coefficients, one regular endpoint and arbitrary deficiency index d, we give a construction for each type and determine the number of possible conditions of each type under the assumption that there are d linearly independent square-integrable solutions for some real value of the spectral parameter. In the separated case our construction yields non-real conditions for all orders greater than two. It is well known that no such conditions exist in the second order case. Our construction gives a direct alternative to the recent construction of Everitt and Markus which uses the theory of symplectic spaces. We believe our construction will prove useful in the spectral analysis of these operators and in obtaining canonical forms of self-adjoint boundary conditions. Such forms are known only in the second order, i.e. Sturm–Liouville, case. Even for regular problems of order four no such forms are available.

Aiping Wang

Jiong Sun

Anton Zettl

Journal of Functional Analysis

《泛函分析杂志》展示了现代泛函分析发挥基本作用的所有科学学科的原创研究论文。发表了各种跨学科领域的科学家的文章。研究领域包括： • 泛函分析的重要应用，包括在其他数学领域的应用 • 泛函分析的新发展 • 对泛函分析中重要问题和挑战的贡献

The Journal of Functional Analysis publishes original research papers that showcase the fundamental role of modern functional analysis across various scientific disciplines. It features articles from scientists in diverse interdisciplinary fields. The areas of research include: • Significant applications of functional analysis in other areas of mathematics • New developments in functional analysis • Contributions to important problems and challenges in functional analysis.

《Journal of Functional Analysis》刊登了现代泛函分析在各科学领域中的原创研究论文，展示了其基本作用。文章涵盖了多个跨学科领域，研究内容包括： • 泛函分析在其他数学领域的重要应用 • 泛函分析的新发展 • 对泛函分析中重要问题和挑战的贡献

Category	Quartile
数学	2
数学, 数学	2

The classification of self-adjoint boundary conditions: Separated, coupled, and mixed

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