Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-28T05:58:20.269Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  23 October 2020

N. Th. Varopoulos
N. Th. Varopoulos
Affiliation:
Université de Paris VI (Pierre et Marie Curie)
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Potential Theory and Geometry on Lie Groups , pp. 585 - 588
Publisher: Cambridge University Press
Print publication year: 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alexopoulos, G. (1992). An application of homogenization theory to harmonic analysis: Harnack inequalities and Riesz transforms to groups of polynomial growth. Canad. J. Math., 44(4), 691–727.CrossRefGoogle Scholar
Borel, A. and Tits, J. (1965). Groupes reductifs. Publ. Math. Inst. Hautes Etudes Sci., 27, 55–150.CrossRefGoogle Scholar
Bott, R. and Tu, L. W. (1982). Differential Forms in Algebraic Topology, Springer.CrossRefGoogle Scholar
Bougerol, P. (1981). Theorem central limit local sur certain groupes de Lie. Ann. Sc. E.N.S., série 4, 14, 403–32.Google Scholar
Bourbaki, N. (1953). Espaces Vectoriels Topologiques, Livre V, Hermann.Google Scholar
Bourbaki, N. (1963). Eléments de Mathématiques, Livre VI, Integration, Hermann.Google Scholar
Bourbaki, N. (1972). Groupes et Algèbres de Lie, Hermann.Google Scholar
Brown, K. S. (1982). Cohomology of Groups, Springer.CrossRefGoogle Scholar
Bruhat, F. and Tits, J. (1972). Groupes réductifs sur un corps local. Publ. Math. Inst. Hautes Etudes Sci., 41, 5–252.CrossRefGoogle Scholar
Cartan, H. (1948). Séminaire ENS, 1948–1963, Tomes 1–16. Faculté de Sciences, Paris.Google Scholar
Cartan, H. and Eilenberg, S. (1956). Homological Algebra, Princeton University Press.Google Scholar
Cassels, J. W. S. (1986). Local Fields, LMS Student Texts 3, Cambridge University Press.CrossRefGoogle Scholar
Cheeger, J. and Ebin, D. G. (1975). Comparison Theorems in Riemannian Geometry, North-Holland.Google Scholar
Chevalley, C. (1951). Théorie de Groupes de Lie, Tome II, Hermann.Google Scholar
Chevalley, C. (1955). Théorie de Groupes de Lie, Tome III, Hermann.Google Scholar
Chung, K. L. (1982). Lectures from Markov Processes to Brownian Motion, Springer.CrossRefGoogle Scholar
Coifman, R. and Weiss, G. (1977). Transference Methods in Analysis, Regional Conference Series in Mathematics 31, American Mathematical Society.CrossRefGoogle Scholar
de Rham, G. (1960). Variétés Differentiables, Hermann.Google Scholar
Dixmier, J. (1957). L’application exponential dans les groupes de Lie resolubles. Bill. Soc. Math. France, 85, 113–21.Google Scholar
Dubrovin, B. A., Fomenko, A. T. and Novikov, S. P. (1990). Modern Geometry – Methods and Applications. Part III , Springer.CrossRefGoogle Scholar
Dunford, N. and Schwartz, J. T. (1958). Linear Operators, Part I, Wiley-Interscience.Google Scholar
Eilenberg, S. and Steenrod, N. (1952). Foundations of Algebraic Topology, Princeton University Press.CrossRefGoogle Scholar
Epstein, D. B. A., Cannon, J. W., Holt, D. F., Paterson, M. S. and Thurston, W. P. (1992). Word Processing in Groups, A. K. Peters/CRC Press.CrossRefGoogle Scholar
Federer, H. (1969). Geometric Measure Theory, Springer.Google Scholar
Feller, W. (1968). An Introduction to Probability Theory and Its Applications, Vols I, II, Wiley.Google Scholar
Gangoli, R. and Varadarajan, V. S. (1980). Harmonic Analysis of Spherical Functions on Real Reductive Groups, Springer.Google Scholar
Gnedenko, B. V. and Kolmogorov, A. N. (1954). Limit Distributions for Sums of Independent Random Variables, Addison–Wesley.Google Scholar
Godement, R. (1958). Topologie Algébrique et Théorie de Faisceaux, Hermann.Google Scholar
Greene, R. E. and Wu, H. (1979). Function Theory on Manifolds Which Possess a Pole, Lecture Notes in Mathematics 699, Springer.CrossRefGoogle Scholar
Greenleaf, F. (1969). Invariant Means on Topological Groups and Their Applications, Van Nostrand.Google Scholar
Greub, W., Halperin, S. and Vanstone, R. (1973). Connections, Curvature and Cohomology, Volume II, Academic Press.Google Scholar
Greub, W., Halperin, S. and Vanstone, R. (1976). Connections, Curvature and Cohomology, Volume III, Academic Press.Google Scholar
Gromov, M. (1981). Groups, polynomial growth and expanding maps. Publ. Math. Inst. Hautes Etudes Sci., 53, 53–78.CrossRefGoogle Scholar
Gromov, M. (1991). Asymptotic invariants of infinite groups. In Niblo, G. and Roller, M., eds., Geometric Group Theory, 2, LMS Lecture Notes Series 182, Cambridge University Press.Google Scholar
Grothendieck, A. (1952). Résume´des resultats essentiels dans la théorie des produits tensoriels topologiques et des espaces nucléaires. Ann. l’Inst. Fourier, 4, 73–112.CrossRefGoogle Scholar
Grothendieck, A. (1958). Espaces Vectoriels Topologiques. Publicação da Sociedade de Matemática de Sao Paulo.Google Scholar
Grünbaum, B. (1967). Convex Polytopes. Springer.Google Scholar
Guivarc’h, Y. (1973). Croissance polynômiale et périodes des fonctions harmoniques. Bull. Soc. Math. France, 101, 333–79.Google Scholar
Hall, M. (1959). The Theory of Groups. Chelsea.Google Scholar
Hebisch, W. (1992). Estimates on the semigroup generated by left-invariant operators on Lie groups. J. reine angew. Math., 423, 1–45.Google Scholar
Helgason, S. (1978). Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press.Google Scholar
Helgason, S. (1984). Groups and Geometric Analysis, Academic Press.Google Scholar
Hicks, N. J. (1971). Notes on Differential Geometry, Van Nostrand.Google Scholar
Hilton, P. J. (1953). Introduction to Homotopy Theory, Cambridge University Press.CrossRefGoogle Scholar
Hilton, P. J. and Wylie, S. (1960). Homology Theory, Cambridge University Press.CrossRefGoogle Scholar
Hirsch, M. W. (1976). Differential Topology, Springer.CrossRefGoogle Scholar
Hochschild, G. (1965). The Structure of Lie Groups, Holden–Day.Google Scholar
Hörmander, L. (1967). Hypoelliptic second order differential equations. Acta Math., 119, 147–71.CrossRefGoogle Scholar
Hörmander, L. (1983). The Analysis of Linear Partial Differential Operators, Volume I, Springer.Google Scholar
Hörmander, L. (1985). The Analysis of Linear Partial Differential Operators, Volume III, Springer.Google Scholar
Humphreys, J. E. (1975). Linear Algebraic Groups, Springer.CrossRefGoogle Scholar
Jacobson, N. (1962). Lie Algebras, Wiley–Interscience.Google Scholar
Jacobson, N. (1989). Basic Algebra, 2nd ed., vols. 1 and 2, Freeman.Google Scholar
Jarchow, H. (1981). Locally Convex Spaces, Teubner.CrossRefGoogle Scholar
Jenkins, J. (1973). Growth of connected locally compact groups. J. Funct. Anal., 12, 113–27.CrossRefGoogle Scholar
Jikov, V. V., Kozlov, S. M. and Oleinik, O. A. (1991). Homogenization of Differential Operators and Integral Functionals, Springer.Google Scholar
Katznelson, Y. (1968). Introduction to Harmonic Analysis, Wiley. (3rd ed. (2004), Cambridge University Press).Google Scholar
Kawada, Y. and Ito, K. (1940). On the probability distribution on a compact group. Proc. Phys. Soc., 22, 977–99.Google Scholar
Knapp, A. W. (1986). Representation Theory of Semisimple Groups. An Overview Based on Examples, Princeton University Press.CrossRefGoogle Scholar
Kobayashi, S. and Nomizu, K. (1963). Foundations of Differential Geometry, Volume 1, Wiley–Interscience.Google Scholar
Kobayashi, S. and Nomizu, K. (1969). Foundations of Differential Geometry, Volume 2. Wiley–Interscience.Google Scholar
Magnus, W., Karass, A. and Solitas, D. (1965). Combinatorial Group Theory, Dover.Google Scholar
Massey, W. S. (1991). A Basic Course in Algebraic Topology, Springer.CrossRefGoogle Scholar
McCleary, J. (2001). User’s Guide to Spectral Sequences, 2nd ed., Cambridge University Press.Google Scholar
Montgomery, D. and Zippin, L. (1955). Topological Transformation Groups, Wiley– Interscience.Google Scholar
Naimark, M. A. (1959). Normed Rings, Noordhoff.Google Scholar
Onischik, A. L. and Vinberg, E. B. (1988). Lie Groups and Algebraic Groups, Springer.Google Scholar
Paterson, A. T. (1988). Amenability, AMS Mathematical Surveys and Monographs 29, American Mathematical Society.CrossRefGoogle Scholar
Pier, J.-P. (1984). Amenable Locally Compact Groups, J. Wiley.Google Scholar
Pontrjagin, L. (1939). Topological Groups, Princeton University Press.Google Scholar
Ragunathan, M. S. (1972). Discrete Subgroups of Lie Groups, Springer.CrossRefGoogle Scholar
Reiter, H. (1968). Classical Harmonic Analysis and Locally Compact Groups, Oxford University Press.Google Scholar
Sagle, A. A. and Walde, R. E. (1973). Introduction to Lie Groups and Lie Algebras, Academic Press.Google Scholar
Schaefer, H. H. (1974). Banach Lattices and Positive Operators, Springer.CrossRefGoogle Scholar
Schwartz, L. (1953). Séminaire Schwartz, 1953–1954. Produits tensoriels topologiques d’espaces vectoriels topologiques, Espaces vectoriels topologiques nucléaires. Applications. Faculté des Sciences de Paris.Google Scholar
Schwartz, L. (1957). Théorie des Distributions, Tome 1, Hermann.Google Scholar
Serre, J.-P. (1965). Lie Algebras and Lie Groups, Benjamin.Google Scholar
Serre, J.-P. (1970). Cohomologie de groupes discrets. Séminaire Bourbaki #399, 1970/71, pp. 337–50.Google Scholar
Steenrod, N. (1951). The Topology of Fiber Bundles, Princeton University Press.CrossRefGoogle Scholar
Szegö, G. (1939). Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ., XXIII.Google Scholar
Varadarajan, V. S. (1974). Lie Groups, Lie Algebras and Their Representations, Prentice-Hall.Google Scholar
Varopoulos, N. Th. (1990). Small time Gaussian estimates of heat diffusion kernels, II. The theory of large deviations. J. Funct. Anal., 93, 1–33.CrossRefGoogle Scholar
Varopoulos, N. Th. (1994a). Diffusion on Lie groups. Canad. J. Math., 46, 438–46.Google Scholar
Varopoulos, N. Th. (1994b). Diffusion on Lie groups, II. Canad. J. Math., 46, 1073–93.Google Scholar
Varopoulos, N. Th. (1996a). The heat kernel on Lie groups. Rev. Mat. Iberoamericana, 12, 147–86.Google Scholar
Varopoulos, N. Th. (1996b). Analysis on Lie groups. Rev. Mat. Iberoamericana, 12, 791–917.CrossRefGoogle Scholar
Varopoulos, N. Th. (1999a). Distance distorsion on Lie groups. In Picardello, M. A. and Woess, W., eds., Random Walks and Discrete Potential Theory, Proceedings, Cortona (1997), Symposia Mathematica 39, Cambridge University Press.Google Scholar
Varopoulos, N. Th. (1999b). Diffusion on Lie groups III. Canad. J. Math., 48, 641–72.Google Scholar
Varopoulos, N. Th. (1999c). Potential theory in conical domains. Math. Proc. Camb. Phil. Soc., 125, 335–84.CrossRefGoogle Scholar
Varopoulos, N. Th. (2000a). Geometric and potential-theoretic results on Lie groups. Canad. J. Math., 52(2), 412–37.CrossRefGoogle Scholar
Varopoulos, N. Th. (2000b). A geometric classification of Lie groups. Rev. Mat. Iberoamericana, 16, 49–136.CrossRefGoogle Scholar
Varopoulos, N. Th. (2001). Potential theory in Lipschitz domains. Canad. J. Math., 53(5), 1057–120.CrossRefGoogle Scholar
Varopoulos, N. Th. (2014). The central limit theorem in Lipschitz domains. Boll. Unione Math. Ital., 7, 103–56.Google Scholar
Varopoulos, N. Th., Saloff-Coste, L. and Coulhon, T. (1992). Analysis and Geometry on Groups, Cambridge University Press.Google Scholar
Warner, F. W. (1971). Foundations of Differentiable Manifolds and Lie Groups, Scott, Foresman and Co. Reprinted 1983, Springer.Google Scholar
Warner, G. (1970). Harmonic Analysis on Semisimple Lie Groups, Vol. I, Springer.Google Scholar
Weil, A. (1953). L’Integration dans les Groupes Topologiques et Applications, Hermann.Google Scholar
Weil, A. (1995). Basic Number Theory, Springer.Google Scholar
Whitney, H. (1958). Elementary structure of real algebraic varieties. Annals Math., 66(3), 545–56.Google Scholar
Williams, D. (1991). Probability with Martingales, Cambridge University Press.CrossRefGoogle Scholar
Woess, W. (2000). Random Walks on Infinite Graphs and Groups, Cambridge Tracts in Mathematics 138, Cambridge University Press.CrossRefGoogle Scholar
Yosida, K. (1970). Functional Analysis, 5th ed. Springer.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • N. Th. Varopoulos, Université de Paris VI (Pierre et Marie Curie)
  • Book: Potential Theory and Geometry on Lie Groups
  • Online publication: 23 October 2020
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • N. Th. Varopoulos, Université de Paris VI (Pierre et Marie Curie)
  • Book: Potential Theory and Geometry on Lie Groups
  • Online publication: 23 October 2020
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • N. Th. Varopoulos, Université de Paris VI (Pierre et Marie Curie)
  • Book: Potential Theory and Geometry on Lie Groups
  • Online publication: 23 October 2020
Available formats
×