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Composition in ultradifferentiable classes

Armin Rainer, Gerhard Schindl (2014)

Studia Mathematica

We characterize stability under composition of ultradifferentiable classes defined by weight sequences M, by weight functions ω, and, more generally, by weight matrices , and investigate continuity of composition (g,f) ↦ f ∘ g. In addition, we represent the Beurling space ( ω ) and the Roumieu space ω as intersection and union of spaces ( M ) and M for associated weight sequences, respectively.

Composition of (E,2)-summing operators

Andreas Defant, Mieczysław Mastyło (2003)

Studia Mathematica

The Banach operator ideal of (q,2)-summing operators plays a fundamental role within the theory of s-number and eigenvalue distribution of Riesz operators in Banach spaces. A key result in this context is a composition formula for such operators due to H. König, J. R. Retherford and N. Tomczak-Jaegermann. Based on abstract interpolation theory, we prove a variant of this result for (E,2)-summing operators, E a symmetric Banach sequence space.

Composition of some singular Fourier integral operators and estimates for restricted X -ray transforms

Allan Greenleaf, Gunther Uhlmann (1990)

Annales de l'institut Fourier

We establish a composition calculus for Fourier integral operators associated with a class of smooth canonical relations C ( T * X 0 ) × ( T * Y 0 ) . These canonical relations, which arise naturally in integral geometry, are such that π : C T * Y is a Whitney fold and ρ : C T * X is a blow-down mapping. If A I m ( C ) , B I m ' ( C t ) , then B A I m + m ' , 0 ( Δ , Λ ) a class of pseudodifferential operators with singular symbols. From this follows L 2 boundedness of A with a loss of 1/4 derivative.

Composition operators and the Hilbert matrix

E. Diamantopoulos, Aristomenis Siskakis (2000)

Studia Mathematica

The Hilbert matrix acts on Hardy spaces by multiplication with Taylor coefficients. We find an upper bound for the norm of the induced operator.

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