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This article overviews the very active past decade in the discipline of Septuagint scholarship, including publications dating from the beginning of 2012 through the end of 2021. It organizes and discusses this activity within numerous categories, beginning with a brief overview of previous disciplinary surveys before moving on to the many new publications that have appeared, including primary texts, commentaries, general introductions, handbooks and companions, and reference works. Further sections give attention to important trends and publications in the main disciplinary journal, as well as in the major conference volumes and series. The second half of the article gives attention to several important areas of development and debate in the discipline, with attention to how it has developed globally over the last ten years. In the course of this discussion, this article, while not exhaustive in scope or coverage, also contributes to the tradition within modern Septuagint scholarship of compiling a bibliography of scholarly publications in the discipline.

While all agree that the language of the Septuagint does not represent a Jewish dialect, scholarship has nevertheless struggled to find ways of discussing the language of the Septuagint without implying a similar idea. Just as the notions of “biblical Greek” and “Jewish Greek” have rightly come under scrutiny, so also must scholars carefully reconsider “Septuagint Greek” and similar sobriquets. While admittedly helpful shorthand, such terminology may unintentionally license—or surreptitiously import—prescriptivist approaches to language that are now widely abandoned in linguistic scholarship. This article presents the ancient historical background to such approaches and surveys problematic terminology common within contemporary scholarship to illustrate its links (or lack thereof) with developments in general linguistics. More up-to-date frameworks, particularly from sociolinguistics, provide better concepts and terminology for discussing the language of the Septuagint. Attention is also given to evaluating the absence of external evidence and matters of style.

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These operators generalize the Hilbert matrix and connect to several problems in function theory such as the Nehari, Carathéodory–Fejér, and Nevanlinna–Pick problems.

This chapter emphasizes the Hilbert-space properties of these operators. In particular, we study the boundedness, norm, adjoint, and spectral properties of Hilbert transforms and how these properties relate to harmonic conjugation and Riemann–Hilbert problems.

These compressed shift operators provide concrete, function-theoretic models for certain Hilbert-space contractions. As a guiding example, this chapter focuses on the compressed shift on the model space corresponding to an atomic inner function.

This chapter covers Bishop operators (T α f)(x) = xf({x + α}) on L2[0, 1]. In the above, α ∈ [0, 1) and {t} denotes the fractional part of t ∈ ℝ. Interest in these operators comes from attempts to provide counterexamples to the invariant subspace problem. We begin with a short survey on the invariant subspace problem and universal operators.

This chapter concerns operators represented by matrices of operators. We examine the norm, spectrum, and invariant subspaces of such operators in terms of their entries.

This chapter surveys Toeplitz operators Tφ : H2 → H2, Tφf = P + (φf), on the Hardy space H2, where φ ∈ L∞(T) and P+ is the orthogonal projection of L2(T) onto H2. We examine the matrix representations of these operators, their spectral properties, and a characterization of them related to the unilateral shift.

This chapter explores the properties of diagonal operators norm, eigenvalues, spectrum, compactness) and extends these concepts to general Hilbert-space operators.