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A CHARACTERIZATION OF WAVE PACKET FRAMES FOR L2 Rd

Yıl 2018, Cilt: 8 Sayı: 2, 353 - 361, 01.12.2018

Öz

In this paper we present necessary and sucient conditions with explicit frame bounds for a nite sum of wave packet frames to be a frame for L2 Rd . Further, we illustrate our results with some examples and applications.

Kaynakça

  • Casazza, P. G., Kutyniok, G., (2012), Finite frames: Theory and Applications, Birkh¨auser.
  • Cerone, P., Dragomir, S.S., (2011), Mathematical Inequalities, CRC Press, New York.
  • Christensen, O., Linear combinations of frames and frame packets, Z. Anal. Anwend., 20 (4), pp. 815. Christensen, O., (2002), An introduction to frames and Riesz bases, Birkh¨auser, Boston.
  • Christensen, O., Rahimi, A., (2008), Frame properties of wave packet systems in L2(R), Adv. Comput. Math., 29, pp. 101–111.
  • Cordoba, A., Fefferman, C., (1978), Wave packets and Fourier integral operators, Comm. Partial Differential Equations, 3 (11), pp. 979–1005.
  • Czaja, W., Kutyniok, G., Speegle, D., (2006), The Geometry of sets of prameters of wave packets, Appl. Comput. Harmon. Anal., 20, pp. 108–125.
  • Heil, C., Walnut, D. (1989), Continuous and discrete wavelet transforms, SIAM Rev., 31 (4), pp. –666.
  • Heil, C., (2011), A basis theory primer, Expanded edition. Applied and Numerical Harmonic Analysis.
  • Birkh¨auser/Springer, New York. Hern´andez, E., Labate, D., Weiss, G., (2002), A unified characterization of reproducing systems generated by a finite family II, J. Geom. Anal., 12 (4), pp. 615–662.
  • Hern´andez, E., Labate, D., Weiss, G., Wilson, E., (2004), Oversampling, quasi-affine frames and wave packets, Appl. Comput. Harmon. Anal., 16, pp. 111–147.
  • Kumar, R., Sah, A. K., (2016), Stability of multivariate wave packet frames for L2(Rn), Boll. Unione Mat. Ital., DOI 10.1007/s40574-016-0106-9.
  • Kumar, R., Sah, A. K., (2016), Matrix Transform of Irregular Weyl-Heisenberg Wave Packet Frames for L2(R), TWMS J. App. Eng. Math., Accepted.
  • Kumar, R., Sah, A. K., (2017), Perturbation of Irregular Weyl-Heisenberg Wave Packet Frames in
  • L2(R), Osaka J. Math., Preprint. Labate, D., Weiss, G., Wilson, E., (2004), An approach to the study of wave packet systems, Contemp. Math., 345, pp. 215–235.
  • Lacey, M., Thiele, C., (1997), Lpestimates on the bilinear Hilbert transform for 2 < p < ∞, Ann. Math., 146, pp. 69–724.
  • Lacey, M., Thiele, C., (1999), On Calder´on’s conjecture, Ann. Math., 149, pp. 475–496.
  • Sah, A.K., (2016) Linear combination of wave packet frame for L2(Rd), Wavelets and Linear Algebra, (2), pp. 19–32.
  • Sah, A.K., Vashisht, L.K., (2014), Hilbert transform of irregular wave packet system for L2(R)
  • Poincare J. Anal. Appl., 1, pp. 9–17. Sah, A.K., Vashisht, L.K., (2015), Irregular Weyl-Heisenberg wave packet frames in L2(R), Bull. Sci. Math. 139, pp. 61–74.
  • Ashok Kumar Sah for the photography and short autobiography, see TWMS J. App. Eng. Math. V.7, N.2, 2017.
Yıl 2018, Cilt: 8 Sayı: 2, 353 - 361, 01.12.2018

Öz

Kaynakça

  • Casazza, P. G., Kutyniok, G., (2012), Finite frames: Theory and Applications, Birkh¨auser.
  • Cerone, P., Dragomir, S.S., (2011), Mathematical Inequalities, CRC Press, New York.
  • Christensen, O., Linear combinations of frames and frame packets, Z. Anal. Anwend., 20 (4), pp. 815. Christensen, O., (2002), An introduction to frames and Riesz bases, Birkh¨auser, Boston.
  • Christensen, O., Rahimi, A., (2008), Frame properties of wave packet systems in L2(R), Adv. Comput. Math., 29, pp. 101–111.
  • Cordoba, A., Fefferman, C., (1978), Wave packets and Fourier integral operators, Comm. Partial Differential Equations, 3 (11), pp. 979–1005.
  • Czaja, W., Kutyniok, G., Speegle, D., (2006), The Geometry of sets of prameters of wave packets, Appl. Comput. Harmon. Anal., 20, pp. 108–125.
  • Heil, C., Walnut, D. (1989), Continuous and discrete wavelet transforms, SIAM Rev., 31 (4), pp. –666.
  • Heil, C., (2011), A basis theory primer, Expanded edition. Applied and Numerical Harmonic Analysis.
  • Birkh¨auser/Springer, New York. Hern´andez, E., Labate, D., Weiss, G., (2002), A unified characterization of reproducing systems generated by a finite family II, J. Geom. Anal., 12 (4), pp. 615–662.
  • Hern´andez, E., Labate, D., Weiss, G., Wilson, E., (2004), Oversampling, quasi-affine frames and wave packets, Appl. Comput. Harmon. Anal., 16, pp. 111–147.
  • Kumar, R., Sah, A. K., (2016), Stability of multivariate wave packet frames for L2(Rn), Boll. Unione Mat. Ital., DOI 10.1007/s40574-016-0106-9.
  • Kumar, R., Sah, A. K., (2016), Matrix Transform of Irregular Weyl-Heisenberg Wave Packet Frames for L2(R), TWMS J. App. Eng. Math., Accepted.
  • Kumar, R., Sah, A. K., (2017), Perturbation of Irregular Weyl-Heisenberg Wave Packet Frames in
  • L2(R), Osaka J. Math., Preprint. Labate, D., Weiss, G., Wilson, E., (2004), An approach to the study of wave packet systems, Contemp. Math., 345, pp. 215–235.
  • Lacey, M., Thiele, C., (1997), Lpestimates on the bilinear Hilbert transform for 2 < p < ∞, Ann. Math., 146, pp. 69–724.
  • Lacey, M., Thiele, C., (1999), On Calder´on’s conjecture, Ann. Math., 149, pp. 475–496.
  • Sah, A.K., (2016) Linear combination of wave packet frame for L2(Rd), Wavelets and Linear Algebra, (2), pp. 19–32.
  • Sah, A.K., Vashisht, L.K., (2014), Hilbert transform of irregular wave packet system for L2(R)
  • Poincare J. Anal. Appl., 1, pp. 9–17. Sah, A.K., Vashisht, L.K., (2015), Irregular Weyl-Heisenberg wave packet frames in L2(R), Bull. Sci. Math. 139, pp. 61–74.
  • Ashok Kumar Sah for the photography and short autobiography, see TWMS J. App. Eng. Math. V.7, N.2, 2017.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Ashok K. Sah Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 8 Sayı: 2

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