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Yıl 2023, Cilt: 44 Sayı: 1, 181 - 187, 26.03.2023

Nuh Durna , Ömer Özdemir

https://doi.org/10.17776/csj.1209529

Öz

Anahtar Kelimeler

Spectra fine spectra generalized difference operator band matrix

Kaynakça

  • [1] Kızmaz H., On certain sequence spaces, Can. Math. Bull., 24(2) (1981) 169–176.
  • [2] Et M., Çolak R., On some generalized difference sequence spaces, Soochow J. Math., 21(4) (1995) 377–386.
  • [3] Baliarsingh P., Some new difference sequence spaces of fractional order and their dual spaces, Appl. Math. Comput., 219(18) (2013) 9737–9742.
  • [4] Bektaş C.A., Et M., Çolak R., Generalized difference sequence spaces and their dual spaces, J. Math. Anal. Appl., 292 (2004) 423–432.
  • [5] Et M., Başarır M., On some new generalized difference sequence spaces, Periodica Math. Hung., 35(3) (1997) 169–175.
  • [6] Malkowsky E., Mursaleen M., Suantai S., The dual spaces of sets of difference sequence sequence spaces of order m and matrix transformations, Acta. Math. Sin. (Engl. Ser.), 23(3) (2007) 521–532.
  • [7] Baliarsingh P., Mursalen M., Rakocevic V., A survey on the spectra of the difference operators over the Banach space, c. RACSAM, 115:57. 84(4) (2021) 1–17.
  • [8] Altay B., Başar F., On the fine spectrum of the difference operator on c_0 and c, Inf. Sci., 168 (2004) 217–224.
  • [9] Altay B., Başar F., The fine spectrum and the matrix domain of the difference operator Δ on the sequence space l_p, (1<p<∞), Commun. Math. Anal., 2(2) (2007) 1–11.
  • [10]Altay B., Başar F., On the fine spectrum of the generalized difference operator B(r,s) over the sequence spaces c_0 and c, Int. J. Math. Math. Sci., 18 (2005) 3005–3013.
  • [11] Akhmedov A.M., Başar F., The fine spectra of the difference operator Δ over the sequence space bv_p, (1≤p<∞), Demonstr. Math., 39(3) (2006) 586–595.
  • [12] Akhmedov A.M., Başar F., On the fine spectra of the difference operator Δ over the sequence space l_p, (1≤p<∞), Acta. Math. Sin. (Engl. Ser.), 23(10) (2007) 1757–1768.
  • [13] Srivastava P.D., Kumar S., On the fine spectrum of the generalized difference operator Δ_v over the sequence space c_0, Commun. Math. Anal., 6(1) (2009) 8–21.
  • [14] Srivastava P.D., Kumar S., Fine spectrum of the generalized difference operator Δ_v on sequence space l_1, Thai. J. Math., 8(2) (2010) 221–233.
  • [15] Akhmedov A.M., El-Shabrawy S.R., On the fine spectrum of the operator Δ_(a,b) over the sequence space c, Comput. Math. Appl., 61 (2011) 2994–3002.
  • [16] Dutta S., Baliarsingh P., On the fine spectra of the generalized rth difference operator Δ_v^r on the sequence space l_1, Appl. Math. Comput., 219 (2012) 1776–1784.
  • [17] Dutta S., Baliarsingh P., On the spectrum of 2-nd order generalized difference operator Δ^2 over the sequence space c_0, Bol. Soc. Paran. Mat., 31(2) (2013) 235–244.
  • [18] Durna N., Yildirim M., Subdivision of the spectra for factorable matrices on c_0, GUJ Sci., 24 (1) (2011) 45-49.
  • [19] Başar F., Durna N., Yildirim M., Subdivisions of the spectra for genarilized difference operator over certain sequence spaces, Thai J. Math., 9(2) (2011) 285–295.
  • [20] Durna N., Subdivision of the spectra for the generalized upper triangular double-band matrices Δ^uv over the sequence spaces c_0 and c, ADYU Sci., 6(1) (2016), 31-43.
  • [21] Das R., On the spectrum and fine spectrum of the upper triangular matrix U(r_1,r_2;s_1,s_2) over the sequence space c_0, Afr. Math., 28 (2017) 841-849.
  • [22] El-Shabrawy S.R., Abu-Janah S.H., Spectra of the generalized difference operator on the sequence spaces bv_0 and h, Linear Multilinear Algebra, 66(8) (2018) 1691–1708.
  • [23] Tripathy B.C., Das R., Fine spectrum of the upper triangular matrix U(r,0,0,s) over the squence spaces c_0 and c, Proyecciones J. Math., 37(1) (2018), 85-101.
  • [24] Durna N., Yildirim M., Kılıç R., Partition of the spectra for the generalized difference operator B(r,s) on thesequence space cs, Cumhuriyet Sci. J., 39(1) (2018) 7–15.
  • [25] Furkan H., Bilgiç H., Altay B., On the fine spectrum of the operator B(r,s,t) over c_0 and c, Comput. Math. Appl., 53(6) (2007) 989–998.
  • [26] Wilansky A., Summability Through Functional Analysis. North-Holland Mathematics Studies, Amsterdam (1984).
  • [27] Goldberg S., Unbounded Linear Operators, New York: McGraw Hill, (1966).
  • [28] Appell J., Pascale E.D., Vignoli A., Nonlinear Spectral Theory, New York Berlin: Walter de Gruyter, (2004).

Spectral Decompositions of the Difference Operator Δ^m over the Sequence Space cs

Yıl 2023, Cilt: 44 Sayı: 1, 181 - 187, 26.03.2023

Nuh Durna , Ömer Özdemir

https://doi.org/10.17776/csj.1209529

Öz

This study aims to bring together some studies on the spectra of difference operators in the literature over the cs sequence space and to provide a basis for related problems. So far, the problem has been solved up to a maximum of 2 orders on the sequence space cs. In this article, we discuss the difference operator Δ^m, represented by a (m+1) banded matrix, which generalizes the difference operators of the form Δ, Δ^2, B(r,s) and B(r,s,t) and we will give its boundedness, spectrum, fine spectrum and some spectral separations over the sequence space cs.

Anahtar Kelimeler

Spectra fine spectra generalized difference operator band matrix

Kaynakça

  • [1] Kızmaz H., On certain sequence spaces, Can. Math. Bull., 24(2) (1981) 169–176.
  • [2] Et M., Çolak R., On some generalized difference sequence spaces, Soochow J. Math., 21(4) (1995) 377–386.
  • [3] Baliarsingh P., Some new difference sequence spaces of fractional order and their dual spaces, Appl. Math. Comput., 219(18) (2013) 9737–9742.
  • [4] Bektaş C.A., Et M., Çolak R., Generalized difference sequence spaces and their dual spaces, J. Math. Anal. Appl., 292 (2004) 423–432.
  • [5] Et M., Başarır M., On some new generalized difference sequence spaces, Periodica Math. Hung., 35(3) (1997) 169–175.
  • [6] Malkowsky E., Mursaleen M., Suantai S., The dual spaces of sets of difference sequence sequence spaces of order m and matrix transformations, Acta. Math. Sin. (Engl. Ser.), 23(3) (2007) 521–532.
  • [7] Baliarsingh P., Mursalen M., Rakocevic V., A survey on the spectra of the difference operators over the Banach space, c. RACSAM, 115:57. 84(4) (2021) 1–17.
  • [8] Altay B., Başar F., On the fine spectrum of the difference operator on c_0 and c, Inf. Sci., 168 (2004) 217–224.
  • [9] Altay B., Başar F., The fine spectrum and the matrix domain of the difference operator Δ on the sequence space l_p, (1<p<∞), Commun. Math. Anal., 2(2) (2007) 1–11.
  • [10]Altay B., Başar F., On the fine spectrum of the generalized difference operator B(r,s) over the sequence spaces c_0 and c, Int. J. Math. Math. Sci., 18 (2005) 3005–3013.
  • [11] Akhmedov A.M., Başar F., The fine spectra of the difference operator Δ over the sequence space bv_p, (1≤p<∞), Demonstr. Math., 39(3) (2006) 586–595.
  • [12] Akhmedov A.M., Başar F., On the fine spectra of the difference operator Δ over the sequence space l_p, (1≤p<∞), Acta. Math. Sin. (Engl. Ser.), 23(10) (2007) 1757–1768.
  • [13] Srivastava P.D., Kumar S., On the fine spectrum of the generalized difference operator Δ_v over the sequence space c_0, Commun. Math. Anal., 6(1) (2009) 8–21.
  • [14] Srivastava P.D., Kumar S., Fine spectrum of the generalized difference operator Δ_v on sequence space l_1, Thai. J. Math., 8(2) (2010) 221–233.
  • [15] Akhmedov A.M., El-Shabrawy S.R., On the fine spectrum of the operator Δ_(a,b) over the sequence space c, Comput. Math. Appl., 61 (2011) 2994–3002.
  • [16] Dutta S., Baliarsingh P., On the fine spectra of the generalized rth difference operator Δ_v^r on the sequence space l_1, Appl. Math. Comput., 219 (2012) 1776–1784.
  • [17] Dutta S., Baliarsingh P., On the spectrum of 2-nd order generalized difference operator Δ^2 over the sequence space c_0, Bol. Soc. Paran. Mat., 31(2) (2013) 235–244.
  • [18] Durna N., Yildirim M., Subdivision of the spectra for factorable matrices on c_0, GUJ Sci., 24 (1) (2011) 45-49.
  • [19] Başar F., Durna N., Yildirim M., Subdivisions of the spectra for genarilized difference operator over certain sequence spaces, Thai J. Math., 9(2) (2011) 285–295.
  • [20] Durna N., Subdivision of the spectra for the generalized upper triangular double-band matrices Δ^uv over the sequence spaces c_0 and c, ADYU Sci., 6(1) (2016), 31-43.
  • [21] Das R., On the spectrum and fine spectrum of the upper triangular matrix U(r_1,r_2;s_1,s_2) over the sequence space c_0, Afr. Math., 28 (2017) 841-849.
  • [22] El-Shabrawy S.R., Abu-Janah S.H., Spectra of the generalized difference operator on the sequence spaces bv_0 and h, Linear Multilinear Algebra, 66(8) (2018) 1691–1708.
  • [23] Tripathy B.C., Das R., Fine spectrum of the upper triangular matrix U(r,0,0,s) over the squence spaces c_0 and c, Proyecciones J. Math., 37(1) (2018), 85-101.
  • [24] Durna N., Yildirim M., Kılıç R., Partition of the spectra for the generalized difference operator B(r,s) on thesequence space cs, Cumhuriyet Sci. J., 39(1) (2018) 7–15.
  • [25] Furkan H., Bilgiç H., Altay B., On the fine spectrum of the operator B(r,s,t) over c_0 and c, Comput. Math. Appl., 53(6) (2007) 989–998.
  • [26] Wilansky A., Summability Through Functional Analysis. North-Holland Mathematics Studies, Amsterdam (1984).
  • [27] Goldberg S., Unbounded Linear Operators, New York: McGraw Hill, (1966).
  • [28] Appell J., Pascale E.D., Vignoli A., Nonlinear Spectral Theory, New York Berlin: Walter de Gruyter, (2004).
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Natural Sciences
Yazarlar

Nuh Durna 0000-0001-5469-7745

Ömer Özdemir 0000-0003-1158-5553

Yayımlanma Tarihi 26 Mart 2023
Gönderilme Tarihi 24 Kasım 2022
Kabul Tarihi 16 Mart 2023
Yayımlandığı Sayı Yıl 2023Cilt: 44 Sayı: 1

Kaynak Göster

APA Durna, N., & Özdemir, Ö. (2023). Spectral Decompositions of the Difference Operator Δ^m over the Sequence Space cs. Cumhuriyet Science Journal, 44(1), 181-187. https://doi.org/10.17776/csj.1209529
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