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We consider $n$ -tuples of commuting operators $a = a_{1}, ..., a_{n}$ on a Banach space with real spectra. The holomorphic functional calculus for $a$ is extended to algebras of ultra-differentiable functions on $ℝ^{n}$ , depending on the growth of $∥ exp (i a \cdot t) ∥$ , $t \in ℝ^{n}$ , when $| t | \to \infty$ . In the non-quasi-analytic case we use the usual Fourier transform, whereas for the quasi-analytic case we introduce a variant of the FBI transform, adapted to ultradifferentiable classes.

Nonlinear maps in spaces of distributions.

T. Gramchev (1992)

Mathematische Zeitschrift

Non-Standard Analysis And Generalized Functions.

Steven M. Moore (1980)

Revista colombiana de matematicas

Normal operators spaces of distributions.

J. B. Cooper (1975)

Collectanea Mathematica

$O^{*}$ -Topologies on the Test Function Algebra

G. Lassner (1975)

Publications du Département de mathématiques (Lyon)

On a space of smooth functions on a convex unbounded set in ℝn admitting holomorphic extension in ℂn

Il’dar Musin, Polina Yakovleva (2012)

Open Mathematics

For some given logarithmically convex sequence M of positive numbers we construct a subspace of the space of rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in ℝn. Due to the conditions on M each function of this space admits a holomorphic extension in ℂn. In the current article, the space of holomorphic extensions is considered and Paley-Wiener type theorems are established. To prove these theorems, some auxiliary results on extensions of holomorphic functions...

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Minimalité de certains espaces fonctionnels et applications à la théorie des opérateurs

Mixed intersections of non quasi-analytic classes.

Moment Sequences for Ultradistributions.

Negative results on the Nash-Moser theorem for Köthe sequences spaces and for spaces of ultradifferentiable functions.

New characterizations for Hankel transformable spaces of Zemanian.

Non-holomorphic functional calculus for commuting operators with real spectrum

Nonlinear maps in spaces of distributions.

Non-Standard Analysis And Generalized Functions.

Normal operators spaces of distributions.

$O^{*}$ -Topologies on the Test Function Algebra

On a space of smooth functions on a convex unbounded set in ℝn admitting holomorphic extension in ℂn

On convergence in some subspaces of generalized functions

On distributions of rapid growth

On E. Borel's Theorem.

On functional equations of complex powers.

On functions with vanishing local derivative

On infinite derivatives of continuous functions

On Multidimensional Generalizations Of Regularly Varying Functions And Tauberian And Abelian Theorems

On regular and absolutely regular distributions in $𝒦_{M}^{'}$ .

On regular $K^{'} M_{P}$ -distributions

Currently displaying 141 – 160 of 279