van den Berg, M.; Gilkey, P. Heat content with singular initial temperature and singular specific heat. (English) Zbl 1320.58014 Potential Anal. 42, No. 1, 1-38 (2015). Reviewer: Mohammed El Aïdi (Bogotá) MSC: 58J32 58J35 58J37 35K20 PDFBibTeX XMLCite \textit{M. van den Berg} and \textit{P. Gilkey}, Potential Anal. 42, No. 1, 1--38 (2015; Zbl 1320.58014) Full Text: DOI arXiv
van den Berg, M.; Dryden, E. B.; Kappeler, T. Isospectrality and heat content. (English) Zbl 1297.58008 Bull. Lond. Math. Soc. 46, No. 4, 793-808 (2014). Reviewer: Peter B. Gilkey (Eugene) MSC: 58J53 58J50 35P10 PDFBibTeX XMLCite \textit{M. van den Berg} et al., Bull. Lond. Math. Soc. 46, No. 4, 793--808 (2014; Zbl 1297.58008) Full Text: DOI arXiv
van den Berg, M.; Gilkey, P.; Kang, H. Neumann heat content asymptotics with singular initial temperature and singular specific heat. (English) Zbl 1311.58015 J. Fixed Point Theory Appl. 14, No. 1, 267-298 (2013). Reviewer: Shu-Yu Hsu (Min-hsiung) MSC: 58J32 58J37 58J35 35K20 PDFBibTeX XMLCite \textit{M. van den Berg} et al., J. Fixed Point Theory Appl. 14, No. 1, 267--298 (2013; Zbl 1311.58015) Full Text: DOI arXiv
van den Berg, M.; Gilkey, P.; Kirsten, K. Heat trace asymptotics with singular weight functions. II. (English) Zbl 1238.58016 J. Geom. Anal. 21, No. 4, 870-901 (2011). Reviewer: Dian K. Palagachev (Bari) MSC: 58J35 35K20 35P99 PDFBibTeX XMLCite \textit{M. van den Berg} et al., J. Geom. Anal. 21, No. 4, 870--901 (2011; Zbl 1238.58016) Full Text: DOI arXiv
van den Berg, M.; Gilkey, Peter; Kirsten, K. Growth of heat trace and heat content asymptotic coefficients. (English) Zbl 1238.58017 J. Funct. Anal. 261, No. 8, 2293-2322 (2011). Reviewer: Dian K. Palagachev (Bari) MSC: 58J35 PDFBibTeX XMLCite \textit{M. van den Berg} et al., J. Funct. Anal. 261, No. 8, 2293--2322 (2011; Zbl 1238.58017) Full Text: DOI arXiv
van den Berg, Michiel; Gilkey, Peter B.; Kirsten, Klaus; Seeley, Robert T. Heat trace asymptotics with singular weight functions. (English) Zbl 1237.58028 Commun. Anal. Geom. 17, No. 3, 529-563 (2009). Reviewer: Dian K. Palagachev (Bari) MSC: 58J37 PDFBibTeX XMLCite \textit{M. van den Berg} et al., Commun. Anal. Geom. 17, No. 3, 529--563 (2009; Zbl 1237.58028) Full Text: DOI arXiv
van den Berg, M.; Gilkey, P.; Seeley, R. Heat content asymptotics with singular initial temperature distributions. (English) Zbl 1143.58013 J. Funct. Anal. 254, No. 12, 3093-3122 (2008). Reviewer: Dian K. Palagachev (Bari) MSC: 58J32 PDFBibTeX XMLCite \textit{M. van den Berg} et al., J. Funct. Anal. 254, No. 12, 3093--3122 (2008; Zbl 1143.58013) Full Text: DOI
van den Berg, M.; Gilkey, P.; Kirsten, K.; Kozlov, V. A. Heat content asymptotics for Riemannian manifolds with Zaremba boundary conditions. (English) Zbl 1114.58022 Potential Anal. 26, No. 3, 225-254 (2007). Reviewer: Georgi E. Karadzhov (Sofia) MSC: 58J35 35P99 PDFBibTeX XMLCite \textit{M. van den Berg} et al., Potential Anal. 26, No. 3, 225--254 (2007; Zbl 1114.58022) Full Text: DOI arXiv
van den Berg, M. Heat content of a Riemannian manifold with a perfect conducting boundary. (English) Zbl 1023.58014 Potential Anal. 19, No. 1, 89-98 (2003). Reviewer: Lubomira Softova (Bari) MSC: 58J35 35K05 58J50 PDFBibTeX XMLCite \textit{M. van den Berg}, Potential Anal. 19, No. 1, 89--98 (2003; Zbl 1023.58014) Full Text: DOI
van den Berg, M.; Lianantonakis, M. Asymptotics for the spectrum of the Dirichlet Laplacian on horn-shaped regions. (English) Zbl 1040.35052 Indiana Univ. Math. J. 50, No. 1, 299-333 (2001). Reviewer: Pavel Burda (Praha) MSC: 35P20 35J25 PDFBibTeX XMLCite \textit{M. van den Berg} and \textit{M. Lianantonakis}, Indiana Univ. Math. J. 50, No. 1, 299--333 (2001; Zbl 1040.35052) Full Text: DOI Link
van den Berg, M.; Gilkey, P. Heat content asymptotics with inhomogeneous Neumann and Dirichlet boundary conditions. (English) Zbl 0990.58019 Potential Anal. 14, No. 3, 269-274 (2001). Reviewer: Novica Blažić (Beograd) MSC: 58J50 58J53 35K05 PDFBibTeX XMLCite \textit{M. van den Berg} and \textit{P. Gilkey}, Potential Anal. 14, No. 3, 269--274 (2001; Zbl 0990.58019) Full Text: DOI
van den Berg, M.; Gilkey, P. The heat content asymptotics of a time-dependent process. (English) Zbl 0984.58012 Proc. R. Soc. Edinb., Sect. A, Math. 130, No. 2, 307-312 (2000). Reviewer: W.Mozgawa (Lublin) MSC: 58J37 PDFBibTeX XMLCite \textit{M. van den Berg} and \textit{P. Gilkey}, Proc. R. Soc. Edinb., Sect. A, Math. 130, No. 2, 307--312 (2000; Zbl 0984.58012) Full Text: DOI
van den Berg, M.; Watson, Simon P. Asymptotics for the spectral heat function and bounds for integrals of Dirichlet eigenfunctions. (English) Zbl 0938.58026 Proc. R. Soc. Edinb., Sect. A, Math. 129, No. 4, 841-854 (1999). Reviewer: M.Puta (Timişoara) MSC: 58J50 58J37 PDFBibTeX XMLCite \textit{M. van den Berg} and \textit{S. P. Watson}, Proc. R. Soc. Edinb., Sect. A, Math. 129, No. 4, 841--854 (1999; Zbl 0938.58026) Full Text: DOI
Van Den Berg, M.; Gilkey, P. B. The heat equation with inhomogeneous Dirichlet boundary conditions. (English) Zbl 0940.58017 Commun. Anal. Geom. 7, No. 2, 279-294 (1999). Reviewer: Maria A.Ragusa (Catania) MSC: 58J37 58J32 35S15 35S35 58J35 PDFBibTeX XMLCite \textit{M. Van Den Berg} and \textit{P. B. Gilkey}, Commun. Anal. Geom. 7, No. 2, 279--294 (1999; Zbl 0940.58017) Full Text: DOI
van den Berg, M.; Levitin, M. Functions of Weierstrass type and spectral asymptotics for iterated sets. (English) Zbl 0867.35068 Q. J. Math., Oxf. II. Ser. 47, No. 188, 493-509 (1996). Reviewer: J.Fleckinger (Toulouse) MSC: 35P20 35B05 35C20 35J05 PDFBibTeX XMLCite \textit{M. van den Berg} and \textit{M. Levitin}, Q. J. Math., Oxf. II. Ser. 47, No. 188, 493--509 (1996; Zbl 0867.35068)
van den Berg, M.; Gilkey, Peter B. Heat invariants for odd-dimensional hemispheres. (English) Zbl 0874.58083 Proc. R. Soc. Edinb., Sect. A 126, No. 1, 187-193 (1996). Reviewer: S.K.Chatterjea (Calcutta) MSC: 58J37 80A20 PDFBibTeX XMLCite \textit{M. van den Berg} and \textit{P. B. Gilkey}, Proc. R. Soc. Edinb., Sect. A, Math. 126, No. 1, 187--193 (1996; Zbl 0874.58083) Full Text: DOI
van den Berg, M. Heat content asymptotics for some open sets with a fractal boundary. (English) Zbl 0851.35050 Cranston, Michael C. (ed.) et al., Stochastic analysis. Proceedings of the Summer Research Institute on stochastic analysis, held at Cornell University, Ithaca, NY, USA, July 11-30, 1993. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 57, 11-22 (1995). Reviewer: P.Kröger (Erlangen) MSC: 35K20 35K05 28A80 PDFBibTeX XMLCite \textit{M. van den Berg}, Proc. Symp. Pure Math. 57, 11--22 (1995; Zbl 0851.35050)
van den Berg, M. Heat content and Brownian motion for some regions with a fractal boundary. (English) Zbl 0812.60068 Probab. Theory Relat. Fields 100, No. 4, 439-456 (1994). Reviewer: J.Bertoin (Paris) MSC: 60J65 35K05 60J45 60J60 PDFBibTeX XMLCite \textit{M. van den Berg}, Probab. Theory Relat. Fields 100, No. 4, 439--456 (1994; Zbl 0812.60068) Full Text: DOI
van den Berg, M.; Desjardins, S.; Gilkey, P. Functoriality and heat content asymptotics for operators of Laplace type. (English) Zbl 0812.58086 Topol. Methods Nonlinear Anal. 2, No. 1, 147-162 (1993). Reviewer: J.Schönenberger-Deuel (Männedorf) MSC: 58J37 58J35 35B40 PDFBibTeX XMLCite \textit{M. van den Berg} et al., Topol. Methods Nonlinear Anal. 2, No. 1, 147--162 (1993; Zbl 0812.58086) Full Text: DOI
van den Berg, M.; Tóth, B. Exponential estimates for the Wiener sausage. (English) Zbl 0717.60093 Probab. Theory Relat. Fields 88, No. 2, 249-259 (1991). Reviewer: M.van den Berg MSC: 60J65 PDFBibTeX XMLCite \textit{M. van den Berg} and \textit{B. Tóth}, Probab. Theory Relat. Fields 88, No. 2, 249--259 (1991; Zbl 0717.60093) Full Text: DOI