The main aim of this paper is to compare two recent approaches for investigating the interspace between the union of Gevrey spaces Gt(U) and the space of smooth functions C∞(U). The first approach in ...the style of Komatsu is based on the properties of two parameter sequences Mp=pτpσ, τ>0, σ>1. The other one uses weight matrices defined by certain weight functions. We prove the equivalence of the corresponding spaces in the Beurling case by taking projective limits with respect to matrix parameters, while in the Roumieu case we need to consider a larger space than the one obtained as the inductive limit of extended Gevrey classes.
Gevrey classes are the most common choice when considering the regularities of smooth functions that are not analytic. However, in various situations, it is important to consider smoothness ...properties that go beyond Gevrey regularity, for example, when initial value problems are ill-posed in Gevrey settings. In this paper, we consider a convenient framework for studying smooth functions that possess weaker regularity than any Gevrey function. Since the available literature on this topic is scattered, our aim is to provide an overview of extended Gevrey regularity, highlighting its most important features. Additionally, we consider related dual spaces of ultra distributions and review some results on micro-local analysis in the context of extended Gevrey regularity. We conclude the paper with a few selected applications that may motivate further study of the topic.
A Paley–Wiener theorem in extended Gevrey regularity Pilipović, Stevan; Teofanov, Nenad; Tomić, Filip
Journal of pseudo-differential operators and applications,
06/2020, Letnik:
11, Številka:
2
Journal Article
Odprti dostop
In this paper we introduce appropriate associated function to the sequence
M
p
=
p
τ
p
σ
,
p
∈
N
,
τ
>
0
,
σ
>
1
, and derive its sharp asymptotic estimates in terms of the Lambert
W
function. These ...estimates are used to prove a Paley–Wiener type theorem for compactly supported functions from extended Gevrey classes. As an application, we discuss properties of the corresponding wave front sets.
Following the well-known theory of Beurling and Roumieu ultradistributions, we investigate new spaces of ultradistributions as dual spaces of test functions which correspond to associated functions ...of logarithmic-type growth at infinity. In the given framework we prove that boundary values of analytic functions with the corresponding logarithmic growth rate towards the real domain are ultradistributions. The essential condition for that purpose, known as stability under ultradifferential operators in the classical ultradistribution theory, is replaced by a weaker condition, in which the growth properties are controlled by an additional parameter. For that reason, new techniques were used in the proofs. As an application, we discuss the corresponding wave front sets.
We consider classes
E
τ
,
σ
(
U
)
of ultradifferentiable functions which are extension of Gevrey classes, and prove that such classes are inverse closed. This result is used to construct an element ...from
E
τ
,
σ
(
U
)
which is not a Gevrey regular function. Furthermore, we show that the singular support of a distribution
u
∈
D
′
(
U
)
related to local regularity in
E
τ
,
σ
(
U
)
coincides with the standard projection of the corresponding wave front set
WF
τ
,
σ
(
u
)
.
The Communist Party of Yugoslavia regarded the interpretation and the commemoration of World War II as one of the most important pillars of the ideology of "brotherhood and unity" and the socialist ...revolution. Accordingly, the issues of the civil war and the nationality and ethnic identity of the perpetrators and victims were suppressed. The article examines war memorials in the Yugoslav Federal Republic of Croatia to show that following the sociopolitical changes that occurred from the mid-1960s, these previously evaded issues became more prominent in public life and began to jeopardize the official policy of remembrance.
Beyond Gevrey regularity Pilipović, Stevan; Teofanov, Nenad; Tomić, Filip
Journal of pseudo-differential operators and applications,
03/2016, Letnik:
7, Številka:
1
Journal Article
Odprti dostop
We define and study classes of smooth functions which are less regular than Gevrey functions. To that end we introduce two-parameter dependent sequences which do not satisfy Komatsu’s condition ...(M.2)’, which implies stability under differential operators within the spaces of ultradifferentiable functions. Our classes therefore have particular behavior under the action of differentiable operators. On a more advanced level, we study microlocal properties and prove that
WF
0
,
∞
(
P
(
D
)
u
)
⊆
WF
0
,
∞
(
u
)
⊆
WF
0
,
∞
(
P
(
D
)
u
)
∪
Char
(
P
)
,
where
u
is a Schwartz distribution,
P
(
D
) is a partial differential operator with constant coefficients and
WF
0
,
∞
is the wave front set described in terms of new regularity conditions. For the analysis we introduce particular admissibility condition for sequences of cut-off functions, and a new technical tool called enumeration.
Romsko stanovništvo živi na hrvatskim područjima od druge polovine XIV. st. Vlasti na hrvatskim područjima započele su krajem XVIII. st. s popisivanjem romskog stanovništva kako bi na temelju tih ...demografskih podataka razumjele položaj Roma. Brojni metodološki problemi prilikom popisivanja Roma predstavljali su određeni izazov hrvatskim vlastima koje su tu metodologiju popisivanja nastojale unaprijediti za vrijeme prvih moderno provedenih popisa stanovništva od 1880. godine. Istraživanjem je obuhvaćena analiza demografskih obilježja romskog stanovništva na sisačko-banovinskom području u razdoblju od 1890. do 1910., ponajprije njihov broj i prostorni razmještaj, vjerska struktura, obrazovna struktura (pismenost) i spolna struktura. Izbor razdoblja temeljio se na dostupnosti arhivske građe iz triju popisa stanovništva koji su provedeni u ovom razdoblju, a koji se čuvaju u Hrvatskom državnom arhivu.
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