The goal of this study gives the approximate
point spectrum, the defect spectrum and the compression spectrum of generalized
difference operator B (r, s) over the class of
convergent series.
[1]. Altay B., Başar F., On the fine spectrum of the generalized difference operator over the sequence spaces and , Int. J. Math. Sci. 18 (2005) 3005-3013.
[2]. Appell J. Pascale E.D., Vignoli A., Nonlinear Spectral Theory. Walter de Gruyter , Berlin , New York, (2004).
[3]. Bilgiç H. and Furkan H., On the fine spectrum of the generalized difference operator over the sequence spaces and , , Nonlinear Anal., 68 ( 2008) 499-506.
[4]. 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.
[5]. Das R., Tripathy B.C., Spectrum and fine spectrum of the lower triangular matrix over the sequence space , Songklanakarin J. Sci. Technol., 38-3 ( 2016) 265-274.
[6]. Das R., On the spectrum and fine spectrum of the upper triangular matrix over the sequence space . Afr. Math. 28-5,6 (2017) 841-849.
[7]. Durna N., Yildirim M., Subdivision of the spectra for factorable matrices on . GUJ Sci ., 24-1 (2011) 45-49.
[8]. Durna N., Subdivision of the spectra for the generalized upper triangular double-band matrices over the sequence spaces and , ADYUSCI, 6-1 ( 2016) 31-43.
[9]. Dutta A., Tripathy B.C., Fine Spectrum of the Generalized Difference Operator over the Class of Convergent Series, Int. J. Anal., 2013, Article ID 630436 (2013), 1-4.
[10]. Goldberg S., Unbounded Linear Operators, McGraw Hill, New York, (1966).
[11]. Paul A., Tripathy B.C., The spectrum of the operator over the sequence spaces and , Hacet. J. Math. Stat., 43-3 ( 2014) 425-434.
[12]. Paul A., Tripathy B.C., The spectrum of the operator over the sequence space , Georgian Math. J., 22-3 (2015) 421-426.
[13]. Tripathy B.C., Das R. Spectrum and fine spectrum of the upper triangular matrix over the squence space, Proyecciones, 34-2 (2015) 107-125.
[14]. Tripathy B.C., Saikia P. On the spectrum of the Cesaro operator on , Math. Slovaca 63-3 (2013) 563-572.
Genelleştirilmiş Fark Operatörü B(r,s) nin cs Dizi Uzayı Üzerinde Spektral Ayrışımı
Year 2018,
Volume: 39 Issue: 1, 7 - 15, 16.03.2018
Bu çalışmanın amacı, yakınsak seriler sınıfında
genelleştirilmiş fark operatörünün yaklaşık nokta spektrumunu, eksik spektrumu
ve sıkıştırma spektrumu vermektir.
[1]. Altay B., Başar F., On the fine spectrum of the generalized difference operator over the sequence spaces and , Int. J. Math. Sci. 18 (2005) 3005-3013.
[2]. Appell J. Pascale E.D., Vignoli A., Nonlinear Spectral Theory. Walter de Gruyter , Berlin , New York, (2004).
[3]. Bilgiç H. and Furkan H., On the fine spectrum of the generalized difference operator over the sequence spaces and , , Nonlinear Anal., 68 ( 2008) 499-506.
[4]. 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.
[5]. Das R., Tripathy B.C., Spectrum and fine spectrum of the lower triangular matrix over the sequence space , Songklanakarin J. Sci. Technol., 38-3 ( 2016) 265-274.
[6]. Das R., On the spectrum and fine spectrum of the upper triangular matrix over the sequence space . Afr. Math. 28-5,6 (2017) 841-849.
[7]. Durna N., Yildirim M., Subdivision of the spectra for factorable matrices on . GUJ Sci ., 24-1 (2011) 45-49.
[8]. Durna N., Subdivision of the spectra for the generalized upper triangular double-band matrices over the sequence spaces and , ADYUSCI, 6-1 ( 2016) 31-43.
[9]. Dutta A., Tripathy B.C., Fine Spectrum of the Generalized Difference Operator over the Class of Convergent Series, Int. J. Anal., 2013, Article ID 630436 (2013), 1-4.
[10]. Goldberg S., Unbounded Linear Operators, McGraw Hill, New York, (1966).
[11]. Paul A., Tripathy B.C., The spectrum of the operator over the sequence spaces and , Hacet. J. Math. Stat., 43-3 ( 2014) 425-434.
[12]. Paul A., Tripathy B.C., The spectrum of the operator over the sequence space , Georgian Math. J., 22-3 (2015) 421-426.
[13]. Tripathy B.C., Das R. Spectrum and fine spectrum of the upper triangular matrix over the squence space, Proyecciones, 34-2 (2015) 107-125.
[14]. Tripathy B.C., Saikia P. On the spectrum of the Cesaro operator on , Math. Slovaca 63-3 (2013) 563-572.
Durna, N., Yıldırım, M., & Kılıç, R. (2018). Partition of the Spectra for the Generalized Difference Operator B(r,s) on the Sequence Space cs. Cumhuriyet Science Journal, 39(1), 7-15. https://doi.org/10.17776/csj.369069