Sampling, Filtering and Sparse Approximations on Combinatorial Graphs

Akhiezer, J.: Theory of Approximation. Ungar, New York (1956)

Belkin, M., Niyogi, P.: Towards a theoretical foundation for Laplacian-based manifold methods. In: Learning Theory. Lecture Notes in Comput. Sci., vol. 3559, pp. 486–500. Springer, Berlin (2005)

Belkin, M., Matveeva, I., Niyogi, P.: Regularization and semi-supervised learning on large graphs. In: Learning Theory. Lecture Notes in Comput. Sci., vol. 3120, pp. 624–638. Springer, Berlin (2004)

Birman, M., Solomyak, M.: Spectral Theory of Selfadjoint Operators in Hilbert Space. Reidel, Dordrecht (1987)

Bremer, J.C., Coifman, R.R., Maggioni, M., Szlam, A.D.: Diffusion wavelet packets. Appl. Comput. Harmon. Anal. 21(1), 95–112 (2006)

Chung, F.R.K.: Spectral Graph Theory. CBMS, vol. 92. AMS, Providence (1994)

Coifman, R.R., Maggioni, M.: Diffusion wavelets. Appl. Comput. Harmon. Anal. 21(1), 53–94 (2006)

Coifman, R.R., Maggioni, M.: Diffusion wavelets for multiscale analysis on graphs and manifolds. In: Wavelets and Splines: Athens 2005. Mod. Methods Math., pp. 164–188. Nashboro Press, Brentwood (2006)

Duffin, R., Schaeffer, A.: A class of nonharmonic Fourier series. Trans. AMS 72, 341–366 (1952)

Frazier, M.W., Torres, R.: The sampling theorem, φ-transform, and Shannon wavelets for ℝ, ℤ, $\mathbb{T}$ , and ℤ N . In: Wavelets: Mathematics and Applications. Stud. Adv. Math., pp. 221–246. CRC, Boca Raton (1994)

Gröchenig, K.: A discrete theory of irregular sampling. Linear Algebra Its Appl. 193, 129–150 (1993)

Herman, G.T., Kuba, A.: Discrete Tomography, Foundations, Algorithms, and Applications. Birkhauser, Basel (1999)

Maggioni, M., Mhaskar, H.N.: Diffusion polynomial frames on metric measure spaces. Appl. Comput. Harmon. Anal. 24(3), 329–353 (2008)

Magyar, A., Stein, E.M., Wainger, S.: Discrete analogues in harmonic analysis: spherical averages. Ann. Math. (2) 155(1), 189–208 (2002)

Mahadevan, S.: Representation Discovery Using Harmonic Analysis. Synthesis Lectures on Artificial Intelligence and Machine Learning. Morgan and Claypool, San Rafael (2008)

Nikolskii, S.M.: Approximation of Functions of Several Variables and Imbedding Theorems. Springer, Berlin (1975)

Peinecke, N., Walter, F., Reiter, M.: Laplace spectra as fingerprints for image recognition. Comput.-Aided Des. 39, 460–476 (2007)

Pesenson, I.: A sampling theorem on homogeneous manifolds. Trans. AMS 352(9), 4257–4270 (2000)

Pesenson, I.: Sampling of Band limited vectors. J. Fourier Anal. Appl. 7(1), 93–100 (2001)

Pesenson, I.: Sampling in Paley-Wiener spaces on combinatorial graphs. Trans. Am. Math. Soc. 360(10), 5603–5627 (2008)

Pesenson, I.: Variational splines and Paley-Wiener spaces on combinatorial graphs. Constr. Approx. 29(1), 1–20 (2009)

Pesenson, I.: Removable sets and eigenvalue and eigenfunction approximations on finite combinatorial graphs. Appl. Comput. Harmon. Anal. (on line)

Pesenson, I., Pesenson, M.: Eigenmaps and minimal and bandlimited immersions of graphs into Euclidean spaces. J. Math. Anal. Appl. (on line)

Pesenson, M., Carey, S., Pesenson, I., et al.: Astronomical Applications of Image Inpainting and Data Dimension Reduction. Astronomical Data Analysis, Software and Systems, XVIII, Quebec (2008)

Pesenson, M., Pesenson, I., Carey, S.: More to astronomical images than meets the eye: data dimension reduction for efficient data organization, retrieval and advanced visualization and analysis of large multitemporal/multispectral data sets. In: 213th American Astronomical Society Meeting, Long Beach, January 2009

Reiter, M., Walter, F., Peinecke, N.: Laplace-Beltrami spectra as “Shape-DNA” for surfaces and solids. Comput.-Aided Des. 38, 342–366 (2006)