Mollifier

DIANA Research Group
DIfferential Algebras and Nonlinear Analysis

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[100]Wave equations on non-smooth space-times
Authors: Hörmann G. , Kunzinger M. , Steinbauer R.
MSC-class: 58J45; 35L05, 35L15, 35D99, 46F30
Journal: submitted
ArXive: 1107.0014
[99]Geometric regularization on Riemannian and Lorentzian manifolds
Authors: Dave S. , Hörmann G. , Kunzinger M.
MSC-class: 58J37; 46F30, 46T30, 35A27, 53C50
Journal: submitted
ArXive: 1107.0010
[98]New energy inequalities for tensorial wave equations on one-sided bounded spacetimes
Authors: Burtscher A. , Grant J. , LeFloch P.
MSC-class:
Journal: submitted
ArXive: 1105.0168
[97]Generalised Fourier integral operator methods for hyperbolic equations with singularities
Authors: Garetto C. , Oberguggenberger M.
MSC-class: 35S30, 46F30, 35B65
Journal: submitted
ArXive: 1104.3035
[96]Symmetrisers and generalised solutions for strictly hyperbolic systems with singular coefficients
Authors: Garetto C. , Oberguggenberger M.
MSC-class:
Journal: submitted
ArXive: 1104.2281
[95]Topological and algebraic structures on the ring of Fermat reals
Authors: Giordano P. , Kunzinger M.
MSC-class: 03H05, 12D, 13J25
Journal: submitted
ArXive: 1104.1492
[94]Manifold-valued generalized functions in full Colombeau spaces
Authors: Kunzinger M. , Nigsch E.
MSC-class: 46F30, 46T30, 26E15
Journal: submitted
ArXive: 1103.5845
[93]Generalized solutions for the Euler-Bernoulli model with Zener viscoelastic foundations and distributional forces
Authors: Hörmann G. , Konjik S. , Oparnica L.
MSC-class: 35D30, 46F30, 35Q74, 26A33, 35A15
Journal: submitted
ArXive: 1102.2148
[92]Wave-type equations of low regularity
Authors: Hanel C.
MSC-class: 83C75, 46F30, 35D05, 35Q75
Journal: Applicable Analysis, iFirst, 2010
ArXive: 1011.4108
[91]Generalized conditional symmetries of evolution equations
Authors: Kunzinger M. , Popovych R.
MSC-class: 35B06; 35K55, 35K57, 35C05
Journal: J. Math. Anal. Appl., to appear
ArXive: 1011.0277
[90]Algebras of generalized functions with smooth parameter dependence
Authors: Burtscher A. , Kunzinger M.
MSC-class: 46F30, 13J25, 46T30
Journal: submitted
ArXive: 1010.5752
[89]Null injectivity estimate under an upper curvature bound
Authors: Grant J. , LeFloch P.
MSC-class:
Journal: submitted
ArXive: 1008.5167
[88]Areas and volumes for null cones
Authors: Grant J.
MSC-class: 53C23, 53C80
Journal: Annales Henri Poincare, to appear
ArXive: 1008.0524
[87]Equivariant homology for pseudo-differential operators
Authors: Dave S.
MSC-class: 58J40, 19D55
Journal: submitted
ArXive: 1005.2282
[86]Inversion of a discontinuous coordinate transformation in general relativity
Authors: Erlacher E. , Grosser M.
MSC-class: 83C35, 46F30, 26B10
Journal: submitted
ArXive: 1003.4245
[85]Notes on generalized pseudo-differential operators
Authors: Dave S.
MSC-class: 58J40, 19D55
Journal: submitted
ArXive: 1005.2279
[84]Optimal regularization processes on complete Riemannian manifolds
Authors: Dave S. , Hörmann G. , Kunzinger M.
MSC-class: 58J37, 46F30, 46T30, 35A27, 35L05
Journal: submitted
ArXive: 1003.3341
[83]Synthetic geometry and generalised functions
Authors: Grant J.
MSC-class:
Journal: Proceedings of GF2009, Vienna, to appear
[82]The Cauchy problem for Schrödinger-type partial differential operators with generalized functions in the principal part and as data
Authors: Hörmann G.
MSC-class: 46F30; 35D99
Journal: Monatshefte f. Mathematik, to appear
ArXive: 0909.5672
[81]A global approach to generalized function algebras
Authors: Dave S.
MSC-class: 46F30; 46T30, 58D99
Journal: Integral Transforms and Spec. Functions, Vol. 20, No. 3, 2009
[80]Rapidly converging approximations and regularity theory
Authors: Dave S.
MSC-class:
Journal: submitted
ArXive: 0906.1374
[79]Is a nonclassical symmetry a symmetry?
Authors: Kunzinger M. , Popovych R.
MSC-class: 35A30; 35C05
Journal: Proc. of 4th Workshop "Group Anal. of Diff. Equ. and Int. Systems", 2009
ArXive: 0903.0821
[78]A global theory of algebras of generalized functions II: tensor distributions
Authors: Grosser M. , Kunzinger M. , Steinbauer R. , Vickers J.
MSC-class: 46F30; 46T30, 26E15, 58B10, 46A17
Journal: submitted
ArXive: 0902.1865
[77]A Note on Distribution Spaces on Manifolds
Authors: Grosser M.
MSC-class: 46T30; 46F05, 46H40
Journal: Novi Sad Journal of Mathematics, to appear
ArXive: 0812.5099
[76]Tensor Valued Colombeau Functions on Manifolds
Authors: Grosser M.
MSC-class: 46F30; 46T30, 53A45
Journal: Banach Center Publications, to appear
ArXive: 0812.3275
[75]Reducible connections and non-local symmetries of the self-dual Yang-Mills equations
Authors: Grant J.
MSC-class:
Journal: Communications in Math. Physics, Vol. 296, 2010
ArXive: 0812.2147
[74]The ADHM construction and non-local symmetries of the self-dual Yang-Mills equations
Authors: Grant J.
MSC-class:
Journal: Communications in Math. Physics, Vol. 296, 2010
ArXive: 0812.2005
[73]Generalized solutions for the Euler-Bernoulli model with distributional forces
Authors: Hörmann G. , Oparnica L.
MSC-class: 35D05; 35D10; 46F30; 35Q72
Journal: J. Math. Anal. Appl., Vol. 357, 2009
ArXive: 0812.1958
[72]A Note on Distributional Semi-Riemannian Geometry
Authors: Steinbauer R.
MSC-class: 83C75; 46T30, 53B30, 46F10, 46F30
Journal: Proc. 12th Serb. Math. Congr., Novi Sad J. Math., Vol. 38, No. 3, 2008
ArXive: 0812.0173
[71]Banach $widetilde{mathbb C}$-algebras
Authors: Vernaeve H.
MSC-class: 46F30
Journal:
ArXive: 0811.1742
[70]Generalized analytic functions on generalized domains
Authors: Vernaeve H.
MSC-class: 46F30
Journal:
ArXive: 0811.1521
[69]On the Geroch-Traschen class of metrics
Authors: Steinbauer R. , Vickers J.
MSC-class: 83C75; 46T30, 53B30, 46F10, 46F30
Journal: Classical and Quantum Gravity, Vol. 26, No. 6
ArXive: 0811.1376
[68]Block diagonalisation of four-dimensional metrics
Authors: Grant J. , Vickers J.
MSC-class: 58A15; 53B99
Journal: Classical and Quantum Gravity, Vol. 26, No. 23, 2009
ArXive: 0809.3327
[67]Classical and Quantum Mechanics via Lie algebras
Authors: Neumaier A. , Westra D.
Type: book
[66]Singular reduction operators in two dimensions
Authors: Kunzinger M. , Popovych R.
MSC-class: 35A30, 35C05, 35K55, 35K55, 35L70
Journal: J. Phys. A: Math. Theor., Vol. 41, No. 505201, 2008
ArXive: 0808.3577
[65]On positivity in algebras of tempered generalized functions
Authors: Mayerhofer E.
MSC-class: 46F30
Journal:
ArXive: 0808.0789
[64]Seismic imaging with the generalized Radon transform and double beamforming: A phase-space transform perspective
Authors: de Hoop M. , Uhlmann G. , van der Hilst R.
MSC-class:
Journal: submitted
[63]Seismic imaging with the generalized Radon transform: A curvelet transform perspective
Authors: de Hoop M. , Smith H. , Uhlmann G. , van der Hilst R.
MSC-class:
Journal: Inverse Problems, Vol. 25, 2009
[62]Local Conservation Laws of Second-Order Evolution Equations
Authors: Popovych R. , Samoilenko A.
MSC-class: 35K55, 35K57, 35A30
Journal: J. Phys. A: Math. Theor., Vol. 41, 2008
ArXive: 0806.2765
[61]Conservation laws and hierarchies of potential symmetries for certain diffusion equations
Authors: Ivanova N. , Popovych R. , Sophocleous C. , Vaneeva O.
MSC-class: 35K57, 35A30
Journal: Physica A, Vol. 388, 2009
ArXive: 0806.1698
[60]Potential Conservation Laws
Authors: Kunzinger M. , Popovych R.
MSC-class: 35A99, 35A30, 35K57, 35K05
Journal: J. Math. Phys., Vol. 49, No. 103506, 2008
ArXive: 0803.1156
[59]Generalized Fourier Integral Operators on spaces of Colombeau type
Authors: Garetto C.
MSC-class: 35S30; 46F30
Journal: Operator theory, Advances and Applications, Birkh. Verlag, Vol. 189, 2008
ArXive: 0803.0284
[58]Symmetry justification of Lorenz´ maximum simplification
Authors: Bihlo A. , Popovych R.
MSC-class:
Journal: Nonlinear Dynamics, to appear
ArXive: 0805.4061
[57]Interactions of delta shock waves in a strictly hyperbolic system of conservation laws
Authors: Nedeljkov M. , Oberguggenberger M.
MSC-class:
Journal: J. Math. Anal. Appl., Vol. 344, 2008
[56]Recent Progress in Special Colombeau Algebras: Geometry, Topology, and Algebra
Authors: Kunzinger M.
MSC-class: 46F30;46T30;46A20;16D25;53B20
Journal: Banach Center Publications, Vol. 88, 2010
ArXive: 0712.4340
[55]Pointwise characterizations in generalized function algebras
Authors: Vernaeve H.
MSC-class: 46F30
Journal: Monatshefte f. Mathematik, Vol. 158, 2009
ArXive: 0712.3464
[54]Reduction operators of linear second-order parabolic equations
Authors: Popovych R.
MSC-class: 35A30, 35C05, 35K05, 35K10
Journal: J. Phys. A, Vol. 41, 2008
ArXive: 0712.2764
[53]Full Algebra of Generalized Functions and Non-Standard Asymptotic Analysis
Authors: Todorov T. , Vernaeve H.
MSC-class: 46F30; 46F10; 03H05; 46S20; 46S10; 35D05
Journal: Logic and Analysis, Vol. 1, No. 3, 2008
ArXive: 0712.2603
[52]Comparison of some solution concepts for linear first-order hyperbolic differential equations with non-smooth coefficients
Authors: Haller S. , Hörmann G.
MSC-class: 35D05,35D10,46F10,46F30
Journal: Publ. de l`Institut Mathematique, Vol. 84, No. 98, 2008
ArXive: 0712.1669
[51]Weak homogeneity in generalized function algebras
Authors: Vernaeve H.
MSC-class: 46F30
Journal: Mathematische Nachrichten, Vol. 283 (10), 2010
ArXive: 0711.2495
[50]Wave equations on space-times of low regularity: Existence results and regularity theory in the framework of generalized function algebras
Authors: Grant J. , Mayerhofer E.
MSC-class: 35L05; 58J45
Journal: Proceedings of GF2007, Bedlewo, 2007
ArXive: 0711.1972
[49]A geometric approach to full Colombeau algebras
Authors: Steinbauer R.
MSC-class: 46T30; 46F30
Journal: Proceedings of GF2007, Bedlewo, to appear
ArXive: 0710.2096
[48]The wave equation on singular space times
Authors: Grant J. , Mayerhofer E. , Steinbauer R.
MSC-class: 83C75, 46F30, 35D05, 35Q75
Journal: Comm. in Mathematical Physics, Vol. 285, No. 2, 2009
ArXive: 0710.2007v1
[47]Geometrical embeddings for distributions into algebras of generalized functions
Authors: Dave S.
MSC-class:
Journal: submitted
ArXive: 0709.2039
[46]Enhanced group analysis of variable coefficient semilinear diffusion equations with a power source
Authors: Popovych R. , Sophocleous C. , Vaneeva O.
MSC-class: 35K57, 35A30, 35C05
Journal: Acta Appl. Math., Vol. 106, 2009
ArXive: 0708.3457
[45]Foundations of the calculus of variations in generalized function algebras
Authors: Konjik S. , Kunzinger M. , Oberguggenberger M.
MSC-class: 49J27, 46F30, 49K27, 37K05
Journal: Acta Appl. Math., Vol. 103, No. 2, 2008
ArXive: 0707.1842
[44]Hilbert $widetilde{mathbb{C}}$-modules: structural properties and applications to variational problems
Authors: Garetto C. , Vernaeve H.
MSC-class: 46F30; 13J99
Journal: Transactions of the American Mathematical Society, Vol. 363, 2011
ArXive: 0707.1104
[43]Internal sets and internal functions in Colombeau theory
Authors: Oberguggenberger M. , Vernaeve H.
MSC-class: 46F30, 46S20
Journal: J. Math. Anal. Appl., Vol. 341
ArXive: 0707.0994
[42]Ideals in the ring of Colombeau generalized numbers
Authors: Vernaeve H.
MSC-class: 16D25; 46F30
Journal: Communications in Algebra, Vol. 38 (6), 2010
ArXive: 0707.0698
[41]Conservation Laws and Potential Symmetries of Linear Parabolic Equations
Authors: Ivanova N. , Kunzinger M. , Popovych R.
MSC-class: 35K05; 35A30; 58J70; 35A15
Journal: Acta Appl. Math., Vol. 100, No. 2, 2008
ArXive: 0706.0443
[40]Sequence spaces with exponent weights. Realizations in Colombeau type algebras
Authors: Delcroix A. , Hasler M. , Pilipovic S. , Valmorin V.
MSC-class: 46A45, 46F30, 46E10, 46A03, 46A13, 46A50
Journal: Dissert. Math., No. 447, 2007
[39]Microlocal Asymptotical Analysis in Algebras of Generalized Functions
Authors: Delcroix A. , Marti J. , Oberguggenberger M.
MSC-class: 35A18, 35A27, 46E10, 46F30, 46T30
Journal: Asymptotic Analysis, Vol. 59, 2008
ArXive: 0704.1077
[38]Real analytic generalized functions
Authors: Pilipovic S. , Scarpalezos D. , Valmorin V.
MSC-class: 35D05, 35L60, 46F30
Journal: Monatsh. Math., Vol. 156, No. 1, 2009
ArXive: math.AP/0702794
[37]Multidimensional integrable systems from deformations of Lie algebra homomorphisms
Authors: Dunajski M. , Grant J. , Strachan I.
MSC-class:
Journal: Journal of Mathematical Physics, Vol. 48, 2007
ArXive: nlin.SI/0702040
[36]Microlocal analysis of generalized pullbacks of Colombeau functions
Authors: Haller S.
MSC-class: 46F30, 35A27, 35A18, 35D10
Journal: Acta Applicandae Mathematicae, Vol. 105, No. 1, 2009
ArXive: math.FA/0701485
[35]Fundamental solutions in the Colombeau framework:applications to solvability and regularity theory
Authors: Garetto C.
MSC-class: 46F30; 35E05
Journal: Acta. Appl. Math., Vol. 102, 2008
ArXive: math.AP/0701344
[34]Global holomorphic representatives of Colombeau holomorphic generalized functions
Authors: Oberguggenberger M. , Pilipovic S. , Valmorin V.
MSC-class: 46F10, 46S10, 35A27
Journal: Monatsh. f. Math., No. 151, 2007
[33]Positivity and positive definiteness in generalized function algebras
Authors: Oberguggenberger M. , Pilipovic S.
MSC-class: 46f30
Journal: J. Math. Anal. Appl., No. 328, 2007
[32]Isomorphisms of algebras of Colombeau generalized functions
Authors: Vernaeve H.
MSC-class: 46F30, 46E25, 54C40, 58A05
Journal: Monatshefte fuer Mathematik, Vol. 162, 2011
ArXive: math.FA/0612646
[31]Colombeau solutions to nonlinear wave equations
Authors: Oberguggenberger M.
Type: tutorial
[30]Homogeneity in generalized function algebras
Authors: Hanel C. , Mayerhofer E. , Pilipovic S. , Vernaeve H.
MSC-class: 46F30
Journal: J. Math. Anal. Appl., Vol. 339, 2008
ArXive: math.GM/0611377
[29]Admissible transformations of nonlinear Schrödinger equations
Authors: Eshragi H. , Kunzinger M. , Popovych R.
MSC-class: 35A30, 35Q55, 58J70, 35C05
Journal: Acta Appl. Math., Vol. 109, 2010
ArXive: math-ph/0611061
[28]An equivariant noncommutative residue
Authors: Dave S.
MSC-class: 58J40, 58J42
Journal: submitted
ArXive: math.AP/0610371
[27]Sheaves of nonlinear generalized functions and manifold-valued distributions
Authors: Kunzinger M. , Steinbauer R. , Vickers J.
MSC-class: 46T30, 46F30, 53B20
Journal: Trans. Amer. Math. Soc., Vol. 361, 2009
ArXive: math.FA/0609358
[26]Closed graph and open mapping theorems for topological $tilde{mathbb C}$-modules and applications
Authors: Garetto C.
MSC-class: 13J99, 46A30, 46F30
Journal: Math. Nachr., to appear
ArXive: math.FA/0608087
[25]Generalized Oscillatory Integrals and Fourier Integral Operators
Authors: Garetto C. , Hörmann G. , Oberguggenberger M.
MSC-class: 46F30
Journal: Proc. Edinburgh Math Soc., Vol. 52, No. 2, 2009
ArXive: math.AP/0607706
[24]Distributional solution concepts for the Euler-Bernoulli beam equation with discontinous coefficients
Authors: Hörmann G. , Oparnica L.
MSC-class: 46F10, 34A36
Journal: Applicable Analysis, Vol. 86, 2007
ArXive: math.AP/0606058
[23]Nonstandard approach to Colombeau theory
Authors: Todorov T.
Type: lecture notes
[22]Spherical completeness of the non-archemedian ring of Colombeau generalized numbers
Authors: Mayerhofer E.
MSC-class: 46F30
Journal: Bull. Inst. Math. Acad. Sinica (NS), Vol. 2, No. 3, 2007
ArXive: math.GM/0604495
[21]On Lorentz geometry in algebras of generalized functions
Authors: Mayerhofer E.
MSC-class: 53B30, 46T30, 46F30, 83C99
Journal: Proceedings of the Royal Society of Edinburgh Sect. A, Vol. 138, No. 4, 2008
ArXive: math-ph/0604052
[20]Divergent type quasilinear Dirichlet problem with singularities
Authors: Pilipovic S. , Scarpalezos D.
MSC-class: 46F30
Journal: Acta Applicandae Mathematicae, Vol. 94, No. 1, 2006
[19]Notes on regularity results in Colombeau algebras
Authors: Oberguggenberger M.
MSC-class:
Journal: Integral Transforms Spec. Funct., Vol. 17, No. 2, 2006
[18]Equalities in Algebras of generalized functions
Authors: Pilipovic S. , Scarpalezos D. , Valmorin V.
MSC-class: 46F30, 46F05, 46S10
Journal: Forum Mathematicum, Vol. 18, No. 5, 2006
[17]Regularity theory in Colombeau algebras
Authors: Oberguggenberger M.
MSC-class:
Journal: Bull. T. CXXXIII Acad. Serbe. Sci. Arts, Cl. Sci. Math. Nat., Sci. Math., Vol. 31, 2006
[16]The use of Generalized Functions and Distributions in General Relativity
Authors: Steinbauer R. , Vickers J.
MSC-class: 8302
Journal: Class. Quantum Grav., Vol. 23, No. 10, 2006
ArXive: gr-qc/0603078
[15]Generalized solutions of the Vlasov-Poisson system with singular data
Authors: Kmit I. , Kunzinger M. , Steinbauer R.
MSC-class: 35A05; 46F30, 35Q72, 82C22
Journal: J. Math. Anal. Appl., Vol. 340, 2008
ArXive: math.AP/0601552
[14]Group invariant Colombeau generalized functions
Authors: Vernaeve H.
MSC-class: 46F30, 35D05
Journal: Monatsh. Math., Vol. 138, 2008
ArXive: math/0512219
[13]On the Characterisation of p-adic Colombeau-Egorov generalized functions by their point values
Authors: Mayerhofer E.
MSC-class: 46F30
Journal: Mathematische Nachrichten, Vol. 280, No. 11, 2007
ArXive: math.FA/0508027
[12]On duality theory and pseudodifferential techniques for Colombeau algebras, generalized delta functionals, kernels and wave front sets
Authors: Garetto C. , Hörmann G.
MSC-class: 46F30, 13J99, 35S30, 35D16
Journal: Bull. Acad. Serbe Cl. Sci., Vol. 31, 2006
ArXive: math.FA/0507222
[11]Evolution systems for paraxial wave equations of Schrödiger-type with non-smooth coefficients
Authors: de Hoop M. , Hörmann G. , Oberguggenberger M.
MSC-class: 35Q99, 46N20
Journal: Jour. Diff. Eqs., Vol. 245, 2008
ArXive: math.AP/0506410
[10]Fourier-integral-operator approximation of solutions to first-order hyperbolic pseudodifferential equations II: microlocal analysis
Authors: Hörmann G. , Le Rosseau J.
MSC-class: 35L05, 35L80,35A21,35S10, 35S30, 86A15
Journal: Jour. Math. Pures Appliquees, Vol. 86, 2006
[9]Pseudodifferential operators with generalized symbols and regularity theory
Authors: Garetto C. , Gramchev T. , Oberguggenberger M.
MSC-class: 35S50; 35S30; 46F10; 46F30; 35D10
Journal: Electron. J. Diff. Eqns., No. 116, 2005
[8]Symmetries and Moduli Spaces of the self dual Yang-Mills Equations
Authors: Grant J.
MSC-class:
Journal: Noncommutative Geometry and Physics, Proc. of the COE Int. Workshop, 2005
[7]Generalized group actions in a global setting
Authors: Konjik S. , Kunzinger M.
MSC-class: 46F30;58E40;46T30; 35A30
Journal: J. Math. Anal. Appl., Vol. 322, No. 1, 2006
ArXive: math.FA/0504061
[6]Group Invariants in Algebras of Generalized Functions
Authors: Konjik S. , Kunzinger M.
MSC-class: 46F30, 58D19, 46T30, 35A30
Journal: Integral Transforms Spec. Funct., Vol. 17, No. 2, 2006
ArXive: math.FA/0504043
[5]Global Gronwall Estimates for Integral Curves on Riemannian Manifolds
Authors: Kunzinger M. , Schichl H. , Steinbauer R. , Vickers J.
MSC-class: 53B21, 53C22, 34A26
Journal: Rev. Mat. Comp., Vol. 19, No. 1, 2006
ArXive: math.DG/0412045
[4]Characterisation of wave front sets by wavelet transforms
Authors: Pilipovic S. , Vuletic M.
MSC-class: 46F12, 43A32
Journal: Tohoku Mathematical Journal, Vol. 58, No. 3, 2006
[3]On Classical Solutions of the Relativistic Vlasov-Klein-Gordon System
Authors: Kunzinger M. , Rein G. , Steinbauer R. , Teschl G.
MSC-class: 35A07, 35Q72, 35Q40, 82C22
Journal: EJDE, Vol. 1, 2005
ArXive: math.AP/0407028
[2]Generalized Connections and Curvature
Authors: Kunzinger M. , Steinbauer R. , Vickers J.
MSC-class: 46F30, 53B05, 46T30
Journal: Math. Proc. Cambridge Philos. Soc., Vol. 355, No. 3, 2005
ArXive: math.FA/0403040
[1]Microlocal hypoellipticity of linear partial differential equations with generalized functions as coefficients
Authors: Hörmann G. , Oberguggenberger M. , Pilipovic S.
MSC-class: 46F30; 35D10
Journal: Trans. Am. Math. Soc., Vol. 358, 2006
ArXive: math.AP/0303248

[START Homepage | Project Description | Publications | Theses]

Last changed January 3, 2007 by M.K. and R.S.