Analytic D-Modules and Applications

Björk, Jan-Erik

doi:10.1007/978-94-017-0717-6

Cited by 184 publications

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“…, since we know from [9], sec.7.2, that the unrestricted limit does not exist, we are sure that the stalk…”

Section: Theorem 41 Assume That Thementioning

confidence: 96%

“…admits an asymptotic development in the basis (1, α (log ) β ), α ∈ Q + * , β ∈ N. This is a consequence of the fact that the sheaf D V [λ]f λ is coherent as a D V -module (see [9], theorem 6.1.9.) Such a coherence property implies (see [14]) the existence of an operator of the form…”

Section: Introductionmentioning

confidence: 99%

“…In this direction we have already mentionned the example of Björk in [9] where f 1 , f 2 are homogeneous polynomials. When f 1 (z 1 , z 2 ) = z 1 and f 2 (z) = z 2 1 + z 2 2 (these are homogeneous, so that the unrestricted limit (1.5) exists for any test form in D 2,0 (C 2 )), one can show that there are test forms in D (n,n−2) (V ), where V is any arbitrary neighborhhood of the origin, for which the rapid decrease of the function λ → J(λ; ϕ)…”

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confidence: 99%

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On asymptotic approximations of the residual currents

Vidras

Yger

1998

Trans. Amer. Math. Soc.

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“…, since we know from [9], sec.7.2, that the unrestricted limit does not exist, we are sure that the stalk…”

Section: Theorem 41 Assume That Thementioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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On asymptotic approximations of the residual currents

Vidras

Yger

1998

Trans. Amer. Math. Soc.

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“…Pour le formalisme et les principaux résultats concernant les Vmodules nous renvoyons aux références de base [4], [5], [16], [17] et [18]. Grâce aux opérations sur les connexions ( [7], ch.…”

Section: Connexion Mixte Associée à Une Famille De Polynômesunclassified

Les connexions hypergéométriques et le théorème de linéarité de T. Terasoma

Maaref¹

1997

Annales De L’institut Fourier

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“…All these characterization results of O suggest a study of the set of PDEpreserving operators for any given set in C containing the homogeneous convolution operators (in this way we deal with rings of infinite type differential operators with variable coefficients and thus with various D-module structures [1] on H Nb ). We obtain a sufficient condition on the sequence in Exp, representing a PDE-preserving operator T for C H , in order that T is PDE-preserving for a larger set (Theorem 1).…”

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confidence: 99%

Rings of PDE-preserving operators on nuclearly entire functions

Petersson

2004

Studia Math.

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Abstract. Let E, F be Banach spaces where F = E or vice versa. If F has the approximation property, then the space of nuclearly entire functions of bounded type, H Nb (E), and the space of exponential type functions, Exp(F ), form a dual pair. The set of convolution operators on H Nb (E) (i.e. the continuous operators that commute with all translations) is formed by the transposes ϕ(D) ≡ t ϕ, ϕ ∈ Exp(F ), of the multiplication operators ϕ : ψ → ϕψ on Exp(F ). A continuous operator T on H Nb (E) is PDE-preserving for a set P ⊆ Exp(F ) if it has the invariance property:The set of PDE-preserving operators O(P) for P forms a ring and, as a starting point, we characterize O(H) in different ways, where H = H(F ) is the set of continuous homogeneous polynomials on F . The elements of O(H) can, in a one-to-one way, be identified with sequences of certain growth in Exp(F ). Further, we establish a kernel theorem: For every continuous linear operator on H Nb (E) there is a unique kernel, or symbol, and we characterize O(H) by describing the corresponding symbol set. We obtain a sufficient condition for an operator to be PDE-preserving for a set P ⊇ H. Finally, by duality we obtain results on operators that preserve ideals in Exp(F ).

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Analytic D-Modules and Applications

Cited by 184 publications

References 0 publications

On asymptotic approximations of the residual currents

On asymptotic approximations of the residual currents

Les connexions hypergéométriques et le théorème de linéarité de T. Terasoma

Rings of PDE-preserving operators on nuclearly entire functions

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