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Characterization of some interpolation spaces (I)

Alessandra Lunardi (1982)

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

Si calcolano alcuni spazi di interpolazione fra spazi di funzioni hölderiane.

Characterization of some interpolation spaces (II)

Alessandra Lunardi (1982)

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

Si caratterizzano alcuni spazi di interpolazione tra spazi di funzioni continue e domini di operatori ellittici del 2° ordine.

Characterization of the convolution operators on quasianalytic classes of Beurling type that admit a continuous linear right inverse

José Bonet, Reinhold Meise (2008)

Studia Mathematica

Extending previous work by Meise and Vogt, we characterize those convolution operators, defined on the space ( ω ) ( ) of (ω)-quasianalytic functions of Beurling type of one variable, which admit a continuous linear right inverse. Also, we characterize those (ω)-ultradifferential operators which admit a continuous linear right inverse on ( ω ) [ a , b ] for each compact interval [a,b] and we show that this property is in fact weaker than the existence of a continuous linear right inverse on ( ω ) ( ) .

Characterization of the domain of an elliptic operator of infinitely many variables in L 2 μ spaces

Giuseppe Da Prato (1997)

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

We consider an elliptic operator associated to a Dirichlet form corresponding to a differential stochastic equation of potential form. We characterize the domain of the operator as a subspace of W 2 , 2 μ , where m u is the invariant measure of the differential stochastic equation.

Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse

B. A. Taylor, R. Meise, Dietmar Vogt (1990)

Annales de l'institut Fourier

Solving a problem of L. Schwartz, those constant coefficient partial differential operators P ( D ) are characterized that admit a continuous linear right inverse on ( Ω ) or 𝒟 ' ( Ω ) , Ω an open set in R n . For bounded Ω with C 1 -boundary these properties are equivalent to P ( D ) being very hyperbolic. For Ω = R n they are equivalent to a Phragmen-Lindelöf condition holding on the zero variety of the polynomial P .

Characterization of unitary processes with independent and stationary increments

Lingaraj Sahu, Kalyan B. Sinha (2010)

Annales de l'I.H.P. Probabilités et statistiques

This is a continuation of the earlier work (Publ. Res. Inst. Math. Sci.45 (2009) 745–785) to characterize unitary stationary independent increment gaussian processes. The earlier assumption of uniform continuity is replaced by weak continuity and with technical assumptions on the domain of the generator, unitary equivalence of the process to the solution of an appropriate Hudson–Parthasarathy equation is proved.

Characterization of weak type by the entropy distribution of r-nuclear operators

Martin Defant, Marius Junge (1993)

Studia Mathematica

The dual of a Banach space X is of weak type p if and only if the entropy numbers of an r-nuclear operator with values in a Banach space of weak type q belong to the Lorentz sequence space s , r with 1/s + 1/p + 1/q = 1 + 1/r (0 < r < 1, 1 ≤ p, q ≤ 2). It is enough to test this for Y = X*. This extends results of Carl, König and Kühn.

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