NEW RESULTS ON SEMICLOSED LINEAR RELATIONS

This paper has triple main objectives. The first objective is an analysis ofsome auxiliary results on closedness and boundednes of linear relations. The seconde objective is to provide some new characterization results on semiclosed linear relations. Here it is shown that the class of semiclosed linear relations is invariant under finite and countable sums, products, and limits. We obtain some fundamental new results as well as a Kato Rellich Theorem for semiclosed linear relations and essentially interesting generalizations. The last objective concern semiclosed linear relation with closed range, where we have particularly established new characterizations of closable linear relation.

Stability Theory for Nullity and Deficiency of Linear Relations

Let A and B be two closed linear relations acting between two Banach spaces X and Y , and let λ be a complex number. We study the stability of the nullity and deficiency of A when it is perturbed by λ B . In particular, we show the existence of a constant ρ > 0 for which both the nullity and deficiency of A remain stable under perturbation by λ B for all λ inside the disk λ < ρ .

On linear relations for special L-values over certain totally real number fields

In this paper, we give linear relations between the Fourier coefficients of a special Hilbert modular form of half integral weight and some arithmetic functions. As a result, we have linear relations for the special [Formula: see text]-values over certain totally real number fields.

Assessing the Manuscripts of Sefer Ḥasidim

This article examines the content and structure of the manuscripts of Sefer Ḥasidim, engaging with ideas concerning its production addressed in Ivan Marcus’s recently published book on Sefer Ḥasidim. Marcus has argued that the book was written piece by piece and not as an integral book and further suggested that each and every manuscript of Sefer Ḥasidim should be taken as a distinct edition of the book prepared by Judah he-Ḥasid. The present study demonstrates that, notwithstanding the gradual process in which Sefer Ḥasidim was written and the great variations among the manuscripts, it is possible to reconstruct a textual process that led to the larger compilations found in the three well-known text editions of Sefer Ḥasidim, represented by MS Parma 3280, MS JTS Boesky 45, and the edition printed in Bologna in 1538. The analysis focuses on the distribution of the text in the manuscripts. While it is difficult to show linear relations among them, the different versions demonstrate a gradual process of growth and enlargement of the material around topical structures. Since most of the material is transmitted in more than one exemplar and few passages appear in one manuscript alone, it is argued that the manuscripts can be linked to show how the material grew from random collections of single paragraphs to topically ordered clusters and into the larger compilations of Sefer Ḥasidim.