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Pregled bibliografske jedinice broj: 986690

On generalized derivative sampling series expansion

Piranashvili, Zurab; Poganj, Tibor
On generalized derivative sampling series expansion // Current Trends in Mathematical Analysis and Its Interdisciplinary Applications / Dutta, Hemen ; Kočinac, Ljubiša ; Srivastava, Hari M. (ur.).
Basel: Springer, 2019. str. 491-519 doi:10.1007/978-3-030-15242-0_14

CROSBI ID: 986690 Za ispravke kontaktirajte CROSBI podršku putem web obrasca

Naslov
On generalized derivative sampling series expansion

Autori
Piranashvili, Zurab ; Poganj, Tibor

Vrsta, podvrsta i kategorija rada
Poglavlja u knjigama, znanstveni

Knjiga
Current Trends in Mathematical Analysis and Its Interdisciplinary Applications

Urednik/ci
Dutta, Hemen ; Kočinac, Ljubiša ; Srivastava, Hari M.

Izdavač
Springer

Grad
Basel

Godina
2019

Raspon stranica
491-519

ISBN
978-3-030-15241-3

Ključne riječi
Whittaker-Kotel'nikov--Shannon sampling theorem ; Derivative sampling ; Exponentially bounded signals ; Entire functions ; Truncation error upper bound ; Harmonizable stochastic process ; Piranashvili process ; Karhunen process ; Loeve process ; Weak sense stationary process ; Mean-square convergence ; Almost sure P convergence.

Sažetak
Master generalized sampling series expansion is presented for entire functions (signals) coming from a class which members satisfy an extended exponential boundedness condition. Firstly, estimates are given for the remainder of Maclaurin series of those functions and consequent derivative sampling results are obtained and discussed. The obtained results are employed in evaluating the related remainder term of signals which occur in sampling series expansion of stochastic processes and random fields (not necessarily stationary or homogeneous) which spectral kernel satisfy the relaxed exponential boundedness. The derived truncation error upper bounds enable to obtain mean-square master generalized derivative sampling series expansion formulae either for harmonizable Piranashvili- type stochastic processes or for random fields. Finally, being the sampling series convergence rate exponential, almost sure P sampling series expansion formulae are presented.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Temeljne tehničke znanosti



POVEZANOST RADA

Ustanove:
Pomorski fakultet, Rijeka

Profili:

Avatar Url Tibor Poganj (autor)

Poveznice na cjeloviti tekst rada:

doi www.springer.com

Citiraj ovu publikaciju:

Piranashvili, Zurab; Poganj, Tibor
On generalized derivative sampling series expansion // Current Trends in Mathematical Analysis and Its Interdisciplinary Applications / Dutta, Hemen ; Kočinac, Ljubiša ; Srivastava, Hari M. (ur.).
Basel: Springer, 2019. str. 491-519 doi:10.1007/978-3-030-15242-0_14
Piranashvili, Z. & Poganj, T. (2019) On generalized derivative sampling series expansion. U: Dutta, H., Kočinac, L. & Srivastava, H. (ur.) Current Trends in Mathematical Analysis and Its Interdisciplinary Applications. Basel, Springer, str. 491-519 doi:10.1007/978-3-030-15242-0_14.
@inbook{inbook, author = {Piranashvili, Zurab and Poganj, Tibor}, year = {2019}, pages = {491-519}, DOI = {10.1007/978-3-030-15242-0\_14}, keywords = {Whittaker-Kotel'nikov--Shannon sampling theorem, Derivative sampling, Exponentially bounded signals, Entire functions, Truncation error upper bound, Harmonizable stochastic process, Piranashvili process, Karhunen process, Loeve process, Weak sense stationary process, Mean-square convergence, Almost sure P convergence.}, doi = {10.1007/978-3-030-15242-0\_14}, isbn = {978-3-030-15241-3}, title = {On generalized derivative sampling series expansion}, keyword = {Whittaker-Kotel'nikov--Shannon sampling theorem, Derivative sampling, Exponentially bounded signals, Entire functions, Truncation error upper bound, Harmonizable stochastic process, Piranashvili process, Karhunen process, Loeve process, Weak sense stationary process, Mean-square convergence, Almost sure P convergence.}, publisher = {Springer}, publisherplace = {Basel} }
@inbook{inbook, author = {Piranashvili, Zurab and Poganj, Tibor}, year = {2019}, pages = {491-519}, DOI = {10.1007/978-3-030-15242-0\_14}, keywords = {Whittaker-Kotel'nikov--Shannon sampling theorem, Derivative sampling, Exponentially bounded signals, Entire functions, Truncation error upper bound, Harmonizable stochastic process, Piranashvili process, Karhunen process, Loeve process, Weak sense stationary process, Mean-square convergence, Almost sure P convergence.}, doi = {10.1007/978-3-030-15242-0\_14}, isbn = {978-3-030-15241-3}, title = {On generalized derivative sampling series expansion}, keyword = {Whittaker-Kotel'nikov--Shannon sampling theorem, Derivative sampling, Exponentially bounded signals, Entire functions, Truncation error upper bound, Harmonizable stochastic process, Piranashvili process, Karhunen process, Loeve process, Weak sense stationary process, Mean-square convergence, Almost sure P convergence.}, publisher = {Springer}, publisherplace = {Basel} }

Časopis indeksira:


  • Web of Science Core Collection (WoSCC)
    • Book Citation Index - Science (BKCI-S)
  • Scopus

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