Harmonic blending approximation
The concept of harmonic Hilbert space \(H_D({\mathbb R} ^n)\) was introduced in [2] as an extension of periodic Hilbert spaces [1], [2], [5], [6]. In [4] we introduced multivariate harmonic Hilbert spaces and studied approximation by exponential-type function in these spaces and derived error bound...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2001-08-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/693 |
| _version_ | 1811294003276021760 |
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| author | Franz-Jürgen Delvos |
| author_facet | Franz-Jürgen Delvos |
| author_sort | Franz-Jürgen Delvos |
| collection | DOAJ |
| description |
The concept of harmonic Hilbert space \(H_D({\mathbb R} ^n)\) was introduced in [2] as an extension of periodic Hilbert spaces [1], [2], [5], [6]. In [4] we introduced multivariate harmonic Hilbert spaces and studied approximation by exponential-type function in these spaces and derived error bounds in the uniform norm for special functions of exponential type which are defined by Fourier partial integrals \(S_b(f)\):
\[
S_b(f)(x)=\int _{ {\mathbb R} ^n } \chi _{[-b,b]}(t) F(t) \exp
(i(t,x)) dt,
\]
\([-b,b]=[-b_1,b_1]\times ... \times [-b_n ,b_n], \quad
b_1>0,...,b_n>0\), where
\(
F(t)\sim \left( {\textstyle\frac 1{2\pi}}\right) ^n\ \int_{{\mathbb
R} ^n}f(x) \exp (-i(x,t))dx \ \in L_2({\mathbb R} ^n) \cap
L_1({\mathbb R} ^n)
\)
is the Fourier transform of \(f \in L_2({\mathbb R} ^n) \cap
C_0({\mathbb R} ^n)\). In this paper we will investigate more general approximation operators \(S_\psi \) in harmonic Hilbert spaces of tensor product type.
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| first_indexed | 2024-04-13T05:10:47Z |
| format | Article |
| id | doaj.art-424d1df93f394bd7a3454560e2ccbdcd |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-04-13T05:10:47Z |
| publishDate | 2001-08-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-424d1df93f394bd7a3454560e2ccbdcd2022-12-22T03:01:02ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2001-08-01302Harmonic blending approximationFranz-Jürgen Delvos0University of Siegen The concept of harmonic Hilbert space \(H_D({\mathbb R} ^n)\) was introduced in [2] as an extension of periodic Hilbert spaces [1], [2], [5], [6]. In [4] we introduced multivariate harmonic Hilbert spaces and studied approximation by exponential-type function in these spaces and derived error bounds in the uniform norm for special functions of exponential type which are defined by Fourier partial integrals \(S_b(f)\): \[ S_b(f)(x)=\int _{ {\mathbb R} ^n } \chi _{[-b,b]}(t) F(t) \exp (i(t,x)) dt, \] \([-b,b]=[-b_1,b_1]\times ... \times [-b_n ,b_n], \quad b_1>0,...,b_n>0\), where \( F(t)\sim \left( {\textstyle\frac 1{2\pi}}\right) ^n\ \int_{{\mathbb R} ^n}f(x) \exp (-i(x,t))dx \ \in L_2({\mathbb R} ^n) \cap L_1({\mathbb R} ^n) \) is the Fourier transform of \(f \in L_2({\mathbb R} ^n) \cap C_0({\mathbb R} ^n)\). In this paper we will investigate more general approximation operators \(S_\psi \) in harmonic Hilbert spaces of tensor product type. https://www.ictp.acad.ro/jnaat/journal/article/view/693 |
| spellingShingle | Franz-Jürgen Delvos Harmonic blending approximation Journal of Numerical Analysis and Approximation Theory |
| title | Harmonic blending approximation |
| title_full | Harmonic blending approximation |
| title_fullStr | Harmonic blending approximation |
| title_full_unstemmed | Harmonic blending approximation |
| title_short | Harmonic blending approximation |
| title_sort | harmonic blending approximation |
| url | https://www.ictp.acad.ro/jnaat/journal/article/view/693 |
| work_keys_str_mv | AT franzjurgendelvos harmonicblendingapproximation |