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On the canonical development of Parseval formulas for singular differential operators

Robert W. Carroll (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Per funzioni opportune f , g si ottiene una formula di Parseval 𝐑 Q , 𝒬 f 𝒬 g λ = Δ Q - 1 / 2 f , Δ Q - 1 / 2 g per operatori differenziali singolari di tipo dell'operatore radiale di Laplace-Beltrami. 𝐑 Q è una funzione spettrale generalizzata di tipo Marčenko e può essere rappresentata per mezzo di un certo nucleo della trasmutazione.

On the eigenvalues of a class of hypo-elliptic operators. IV

Johannes Sjöstrand (1980)

Annales de l'institut Fourier

Let P be a selfadjoint classical pseudo-differential operator of order > 1 with non-negative principal symbol on a compact manifold. We assume that P is hypoelliptic with loss of one derivative and semibounded from below. Then exp ( - t P ) , t 0 , is constructed as a non-classical Fourier integral operator and the main contribution to the asymptotic distribution of eigenvalues of P is computed. This paper is a continuation of a series of joint works with A. Menikoff.

Once more about the monotonicity of the Temple quotients

Drahoslava Janovská, Ivo Marek (1984)

Aplikace matematiky

A new proof of the monotonicity of the Temple quotients for the computation of the dominant eigenvalue of a bounded linear normal operator in a Hilbert space is given. Another goal of the paper is a precise analysis of the length of the interval for admissible shifts for the Temple quotients.

Quasi *-algebras and generalized inductive limits of C*-algebras

Giorgia Bellomonte, Camillo Trapani (2011)

Studia Mathematica

A generalized procedure for the construction of the inductive limit of a family of C*-algebras is proposed. The outcome is no more a C*-algebra but, under certain assumptions, a locally convex quasi *-algebra, named a C*-inductive quasi *-algebra. The properties of positive functionals and representations of C*-inductive quasi *-algebras are investigated, in close connection with the corresponding properties of positive functionals and representations of the C*-algebras that generate the structure....

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