The theorem of iterates for elliptic and non-elliptic operators

Fürdös, Stefan; Schindl, Gerhard

doi:10.1016/j.jfa.2022.109554

Cited by 6 publications

(7 citation statements)

References 56 publications

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“…Consider the sequences with . Then ( 7.4 ) is valid (with and k such that ) as it is shown in [ 3 , Example 6.6 (1)].…”

Section: Growth and Regularity Conditions For Associated N-functionsmentioning

confidence: 70%

“…( 7.3 ) has already appeared (crucially) in different contexts; it is denoted by in [ 9 ] and in [ 18 ]; by in [ 15 ] and by in [ 3 ].…”

Section: Growth and Regularity Conditions For Associated N-functionsmentioning

confidence: 99%

“…2 all relevant definitions concerning weight sequences and (associated) weight functions are given and in Sect. 3 we recall and introduce the notions of (associated) N-functions. In Sect.…”

Section: Introductionmentioning

confidence: 99%

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On Orlicz classes defined in terms of associated weight functions

Schindl

2024

Monatsh Math

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N-functions and their growth and regularity properties are crucial in order to introduce and study Orlicz classes and Orlicz spaces. We consider N-functions which are given in terms of so-called associated weight functions. These functions are frequently appearing in the theory of ultradifferentiable function classes and in this setting additional information is available since associated weight functions are defined in terms of a given weight sequence. We express and characterize several known properties for N-functions purely in terms of weight sequences which allows to construct (counter-) examples. Moreover, we study how for abstractly given N-functions this framework becomes meaningful and finally we establish a connection between the complementary N-function and the recently introduced notion of the so-called dual sequence.

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“…Consider the sequences with . Then ( 7.4 ) is valid (with and k such that ) as it is shown in [ 3 , Example 6.6 (1)].…”

Section: Growth and Regularity Conditions For Associated N-functionsmentioning

confidence: 70%

“…( 7.3 ) has already appeared (crucially) in different contexts; it is denoted by in [ 9 ] and in [ 18 ]; by in [ 15 ] and by in [ 3 ].…”

Section: Growth and Regularity Conditions For Associated N-functionsmentioning

confidence: 99%

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On Orlicz classes defined in terms of associated weight functions

Schindl

2024

Monatsh Math

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“…Since then several papers using weight matrices have been published. We mention, for instance, [ 4 , 9 , 10 , 13 ], and the references therein. However, the characterization of inclusion relations in global classes of ultradifferentiable functions, i.e.…”

Section: Introductionmentioning

confidence: 99%

On the Inclusion Relations of Global Ultradifferentiable Classes Defined by Weight Matrices

Boiti,

Jornet,

Oliaro

et al. 2024

Mediterr. J. Math.

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We study and characterize the inclusion relations of global classes in the general weight matrix framework in terms of growth relations for the defining weight matrices. We consider the Roumieu and Beurling cases, and as a particular case, we also treat the classical weight function and weight sequence cases. Moreover, we construct a weight sequence which is oscillating around any weight sequence which satisfies some minimal conditions and, in particular, around the critical weight sequence $$(p!)^{1/2}$$ ( p ! ) 1 / 2 , related with the non-triviality of the classes. Finally, we also obtain comparison results both on classes defined by weight functions that can be defined by weight sequences and conversely.

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“…Since then several papers using weight matrices have been published. We mention, for instance, [4,9,10,13], and the references therein. However, the characterization of inclusion relations in global classes of ultradifferentiable functions, i.e.…”

Section: Introductionmentioning

confidence: 99%

Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting

Boiti

Jornet

Oliaro

et al. 2020

Banach J. Math. Anal.

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We prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine also the corresponding coefficient spaces, thus extending the previous work by Langenbruch. As a consequence, we give very general conditions for these spaces to be nuclear. In particular, we obtain the corresponding results for spaces defined by weight functions.

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The theorem of iterates for elliptic and non-elliptic operators

Cited by 6 publications

References 56 publications

On Orlicz classes defined in terms of associated weight functions

On Orlicz classes defined in terms of associated weight functions

On the Inclusion Relations of Global Ultradifferentiable Classes Defined by Weight Matrices

Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting

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