Copy number variations (CNVs) involving the JAG1 gene are rare and infrequently reported in the scientific literature. Recently, a generally healthy young patient presenting with a history of behavioural concerns was referred to us. Herein, we discuss the patient, a 7-year-old female possessing a 0.797 Mb microduplication within the short arm of chromosome 20 at band 12.2. The patient generates considerable curiosity due to the rarity of her case, which includes a de novo partial duplication involving the JAG1 gene. The patient exhibits a wide range of symptoms including facial dysmorphism (dolichocephaly, round face, tented philtrum, anteverted nares, and micrognathia), clinodactyly, and an inborn congenital heart defect. She presented with behavioural concerns including ADHD-I, SPD, motor clumsiness, and poor self-regulation. Deletions in JAG1 are often linked to Alagille Syndrome; however, complete duplications have not been specifically identified as disease-causing. JAG1 mutations are reported alongside various clinical features including facial dysmorphology, heart defects, vertebral abnormalities, and ocular dysmorphic features (strabismus, epicanthal folds, and slanted palpebral fissures). This particular microduplication is rare, and thus, limited data exist regarding its significance. To our knowledge, most reported duplications are larger than 0.797 Mb. This may define a critical region causing phenotypical changes in some patient cases.

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There are several notions of positive definiteness for functions on topological groups, the two of which are: Bochner type positive definite functions and integrally positive definite functions. The class P(F) of positive definite functions for the class F can be defined more generally and it is interesting to observe that a change in F produces a different class P(F) of positive definite functions. The purpose of this paper is to study the functions in P(LP(G)) which are positive definite for the class LP(G) (1 ≦ p < ∞), where G is a compact or locally compact group. The relevant information about the class P(F) can be found in [1; 2; 3 and 8].