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Overview of the topical collection: harmonic analysis on combinatorial graphs. (English) Zbl 1484.42002

Summary: This topical collection “Harmonic Analysis on Combinatorial Graphs” contains 20 papers devoted to a very broad range of themes written by pure and applied mathematician. The first part of this overview is aiming at mathematicians with no experience in harmonic analysis on combinatorial graphs and represents a very concise introduction to this emerging field. The second part contains a brief summary of papers in the topical collection.

MSC:

42-06 Proceedings, conferences, collections, etc. pertaining to harmonic analysis on Euclidean spaces
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42C15 General harmonic expansions, frames
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
05C99 Graph theory
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C10 Planar graphs; geometric and topological aspects of graph theory

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[1] Anis, A., Gadde, A., Ortega, A.: Towards a sampling theorem for signals on arbitrary graphs. In: Acoustics, Speech and Signal Processing (ICASSP). IEEE International Conference on. IEEE, vol. 2014, pp. 3864-3868 (2014)
[2] Avrachenkov, K.; Bobu, A.; Dreveton, M., Higher-order spectral clustering for geometric graphs, J. Fourier Anal. Appl., 27, 22 (2021) · Zbl 1466.62349
[3] Barbecki, C.: Codes, cubes and graph designs. J. Fourier Anal. Appl. 27(5), Paper No. 81 (2021) · Zbl 1472.05030
[4] Bezuglyi, S.; Jörgensen, P., Harmonic analysis invariants for infinite graphs via operators and algorithms, J. Fourier Anal. Appl., 27, 34 (2021) · Zbl 1462.05261
[5] Brown, L., Sequences of well-distributed vertices on graphs and spectral bounds on optimal transport, J. Fourier Anal. Appl., 27, 36 (2021) · Zbl 1462.05192
[6] Chen, S.; Varma, R.; Sandryhaila, A.; Kovacevich, J., Discrete signal processing on graphs: sampling theory, IEEE Trans. Signal Process., 63, 24, 6510-6523 (2014) · Zbl 1395.94094
[7] Cheng, C.; Jiang, Y.; Sun, Q., Spatially distributed sampling and reconstruction, Appl. Comput. Harmon. Anal., 47, 1, 109-148 (2019) · Zbl 1435.94164
[8] Calder, J.; Drenska, N., Asymptotically optimal strategies for online prediction with history-dependent experts, J. Fourier Anal. Appl., 27, 20 (2021) · Zbl 1459.91171
[9] Cavoretto, R., De Rossi, A., Erb, W.: Partition of unity methods for signal processing on graphs. J. Fourier Anal. Appl. 27(4), Paper No. 66 (2021) · Zbl 1473.65054
[10] Chen, E., DeJong, J., Halverson, T., Shuman, D.: Signal processing on the permutahedron: tight spectral frames for ranked data analysis. J. Fourier Anal. Appl. 27(4), Paper No. 70 (2021) · Zbl 1471.94009
[11] Cloninger, A., Mhaskar, H.: A low discrepancy sequence on graphs. J. Fourier Anal. Appl. 27(5), Paper No. 76 (2021) · Zbl 1472.05136
[12] Cloninger, A.; Li, H.; Saito, N., Natural graph wavelet packet dictionaries, J. Fourier Anal. Appl., 27, 41 (2021) · Zbl 1462.65229
[13] De Vito, E.; Kereta, Z.; Naumova, V.; Rosasco, L.; Vigogna, S., Construction and Monte Carlo estimation of wavelet frames generated by a reproducing kernel, J. Fourier Anal. Appl., 27, 37 (2021) · Zbl 1462.42051
[14] Erb, W.: Graph signal interpolation with positive definite graph basis functions, arxiv:1912.02069 (2019)
[15] Fang, Q., Shin, C., Sun, Q.: Polynomial control on weighted stability bounds and inversion norms of localized matrices on simple graphs. J. Fourier Anal. Appl. 27(5), Paper No. 83 (2021). doi:10.1007/s00041-021-09864-9 · Zbl 1492.05087
[16] Filbir, F.; Krahmer, F.; Melnyk, O., On recovery guarantees for angular synchronization, J. Fourier Anal. Appl., 27, 31 (2021) · Zbl 1470.90065
[17] Führ, H.; Pesenson, I., Poincaré and Plancherel-Polya inequalities in harmonic analysis on weighted combinatorial graphs, SIAM J. Discret. Math., 27, 4, 2007-2028 (2013) · Zbl 1307.05094
[18] Ghandehari, M.; Guillot, D.; Hollingsworth, K., Gabor-type frames for signal processing on graphs, J. Fourier Anal. Appl., 27, 25 (2021) · Zbl 1464.42025
[19] Haeseler, S., Keller, M.: Generalized solutions and spectrum for Dirichlet forms on graphs. In: Random Walks, Boundaries and Spectra. Progr. Probab., vol. 64, pp. 181-199. Birkhäuser/Springer Basel AG, Basel (2011) · Zbl 1227.47023
[20] Haeseler, S.; Keller, M.; Lenz, D.; Wojciechowski, R., Laplacians on infinite graphs: Dirichlet and Neumann boundary conditions, J. Spectr. Theory, 2, 4, 397-432 (2012) · Zbl 1287.47023
[21] Hua, B.; Masamune, J.; Wojciechowski, RK, Essential self-adjointness and the \(L^2\)-Liouville property, J. Fourier Anal. Appl., 27, 26 (2021) · Zbl 1461.35079
[22] Huang, C., Zhang, Q., Huang, J., Yang, L.: Approximation theorems on graphs. J. Approx. Theory 270, Paper No. 105620 (2021). doi:10.1016/j.jat.2021.105620 · Zbl 1473.05296
[23] Jiang, Q.; Lan, T.; Okoudjou, K.; Strichartz, R.; Sule, S.; Venkat, S.; Wang, X., Sobolev orthogonal polynomials on the Sierpinski gasket, J. Fourier Anal. Appl., 27, 38 (2021) · Zbl 1462.42045
[24] Kileel, J., Moscovich, A., Zelesko, N., Singer, A.: Manifold learning with arbitrary norms. J. Fourier Anal. Appl. 27(5), Paper No. 82 (2021) · Zbl 07395100
[25] Leus, G.; Segarra, S.; Ribeiro, A.; Marques, A., The dual graph shift operator: identifying the support of the frequency domain, J. Fourier Anal. Appl., 27, 49 (2021) · Zbl 1467.94012
[26] Linderman, G.; Steinerberger, S., Numerical integration on graphs: where to sample and how to weigh, Math. Comput., 89, 324, 1933-1952 (2020) · Zbl 1437.05143
[27] Mohar, B.: Some applications of Laplace eigenvalues of graphs. In: Hahn, G., Sabidussi, G. (eds.) Graph Symmetry: Algebraic Methods and Applications (Proc. Montreal 1996), volume 497 of Adv. Sci. Inst. Ser. C. Math. Phys. Sci., pp. 225-275. Dordrecht, Kluwer (1997) · Zbl 0883.05096
[28] Narang, S.K., Gadde, A., Ortega, A.: Signal processing techniques for interpolation in graph structured data. In: Acoustics, Speech and Signal Processing (ICASSP), IEEE International Conference on. IEEE, pp. 5445-5449 (2013)
[29] Ortega, A.; Frossard, P.; Kovacevic, J.; Moura, JMF; Vandergheynst, P., Graph signal processing: overview, challenges and applications, Proc. IEEE, 106, 808-828 (2018)
[30] Pesenson, IZ; Pesenson, MZ, Graph signal sampling and interpolation based on clusters and averages, J Fourier Anal Appl., 27, 39 (2021) · Zbl 1462.42057
[31] Pesenson, I., Sampling of band limited vectors, J. Fourier Anal. Appl., 7, 1, 93-100 (2001) · Zbl 0998.42025
[32] Pesenson, I., Sampling in Paley-Wiener spaces on combinatorial graphs, Trans. Am. Math. Soc., 36, 10, 5603-5627 (2008) · Zbl 1165.42010
[33] Pesenson, IZ, Variational splines and Paley-Wiener spaces on combinatorial graphs, Constr. Approx., 29, 1, 1-21 (2009) · Zbl 1180.42026
[34] Pesenson, IZ; Pesenson, MZ, Sampling, filtering and sparse approximations on combinatorial graphs, J. Fourier Anal. Appl., 16, 6, 921-942 (2010) · Zbl 1218.42021
[35] Pesenson, I. Z., Pesenson, M. Z., Führ, H.: Cubature formulas on combinatorial graphs, arxiv:1104.0963 (2011) · Zbl 1307.05094
[36] Pesenson, I.: Sampling solutions of Schrödinger equations on combinatorial graphs, arxiv:1502.07688v2 [math.SP] (2015)
[37] Pesenson, I. Z.: Sampling by averages and average splines on Dirichlet spaces and on combinatorial graphs. In: Excursions in Harmonic Analysis, Appl. Numer. Harmon. Anal., vol. 6, pp. 243-268. Birkhäuser/Springer, Cham (2021) · Zbl 1481.94074
[38] Puy, G.; Tremblay, N.; Gribonval, R.; Vandergheynst, P., Random sampling of bandlimited signals on graphs, Appl. Comput. Harmon. Anal., 44, 2, 446-475 (2018) · Zbl 1391.94367
[39] Strichartz, R., Half sampling on bipartite graphs, J. Fourier Anal. Appl., 22, 5, 1157-1173 (2016) · Zbl 1348.05129
[40] Tanaka, Y., Eldar, Y. C., Ortega, A., Cheung, G.: Sampling signals on graphs: from theory to applications. arxiv:2003.03957v4 [eess.SP] (2020)
[41] Weidmann, J., Linear Operators in Hilbert Spaces, Graduate Texts in Mathematics (1980), New York: Springer, New York · Zbl 0434.47001
[42] Wojciechowski, RK, Stochastic completeness of graphs: bounded Laplacians, intrinsic metrics, volume growth and curvature, J. Fourier Anal. Appl., 27, 30, 1-45 (2021) · Zbl 1462.05167
[43] Xiao, Y.; Zhuang, X., Adaptive directional Haar tight framelets on bounded domains for digraph signal representations, J. Fourier Anal. Appl., 27, 7, 1-26 (2021) · Zbl 1459.42049
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.