Lars Hörmander | Academic Influence

Lars Hörmander's AcademicInfluence.com Rankings

Lars Hörmander

Mathematics

#77

World Rank

#218

Historical Rank

Measure Theory

#109

World Rank

#174

Historical Rank

mathematics Degrees

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Mathematics

Lars Hörmander's Degrees

PhD Mathematics Stockholm University

Why Is Lars Hörmander Influential?

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According to Wikipedia, Lars Valter Hörmander was a Swedish mathematician who has been called "the foremost contributor to the modern theory of linear partial differential equations". Hörmander was awarded the Fields Medal in 1962 and the Wolf Prize in 1988. In 2006 he was awarded the Steele Prize for Mathematical Exposition for his four-volume textbook Analysis of Linear Partial Differential Operators, which is considered a foundational work on the subject.

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Lars Hörmander's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

The analysis of linear partial differential operators (1990) (8608)
Linear Partial Differential Operators (1963) (2569)
Hypoelliptic second order differential equations (1967) (2271)
An introduction to complex analysis in several variables (1973) (2099)
The Analysis of Linear Partial Differential Operators III (2007) (1554)
The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis (1983) (1537)
Fourier integral operators. I (1995) (1511)
Estimates for translation invariant operators inLp spaces (1960) (1312)
The Analysis of Linear Partial Differential Operators IV (1985) (977)
The spectral function of an elliptic operator (1968) (822)
Lectures on Nonlinear Hyperbolic Differential Equations (1997) (789)
Notions of Convexity (1994) (718)
L2 estimates and existence theorems for the $$\bar \partial $$ operator (1965) (668)
Fourier integral operators. II (1972) (569)
The weyl calculus of pseudo‐differential operators (1979) (481)
Pseudo-differential Operators and Non-elliptic Boundary Problems (1966) (435)
On the theory of general partial differential operators (1955) (329)
Analysis of Linear Partial Differential Operators II (2005) (320)
The boundary problems of physical geodesy (1976) (303)
The Analysis of Linear Partial Differential Operators II: Differential Operators with Constant Coefficients (1983) (293)
Distribution theory and Fourier analysis (1990) (270)
Oscillatory integrals and multipliers onFLp (1973) (261)
Asymptotic properties of solutions of differential equations with simple characteristics (1976) (251)
Pseudo-Differential Operators (1965) (210)
Uniqueness theorems and wave front sets for solutions of linear differential equations with analytic coefficients (1971) (209)
On the division of distributions by polynomials (1958) (178)
On the existence and the regularity of solutions of linear pseudo-differential equations (1971) (175)
Lp Estimates for (Pluri-) Subharmonic Functions. (1967) (174)
Intermediate Schauder estimates (1980) (169)
The Cauchy problem for differential equations with double characteristics (1977) (168)
Symplectic classification of quadratic forms, and general Mehler formulas (1995) (167)
Generators for some rings of analytic functions (1967) (157)
A uniqueness theorem of Beurling for Fourier transform pairs (1991) (152)
North-Holland Mathematical Library (2005) (130)
The lifespan of classical solutions of non-linear hyperbolic equations (1987) (119)
On the asymptotic distribution of the eigenvalues of pseudodifferential operators inRn (1979) (116)
On the Range of Convolution Operators (1962) (107)
The existence of wave operators in scattering theory (1976) (100)
On the existence of real analytic solutions of partial differential equations with constant coefficients (1973) (97)
Differential operators with constant coefficients (1983) (92)
On the singularities of solutions of partial differential equations (1970) (88)
Uniform Approximation on Compact Sets in $\mathsf{C}^n$. (1968) (84)
A class of hypoelliptic pseudodifferential operators with double characteristics (1975) (76)
Differential operators of principal type (1960) (68)
On interior regularity of the solutions of partial differential equations (1958) (65)
Quadratic hyperbolic operators (1991) (64)
A remark on the characteristic Cauchy problem (1990) (64)
On the regularity of the solutions of boundary problems (1958) (62)
On the uniqueness of the Cauchy problem under partial analyticity assumptions (1997) (61)
The transmission property. (1990) (60)
On the Nash-Moser implicit function theorem (1985) (58)
Propagation of Singularities and Semi-Global Existence Theorems for (Pseudo)-Differential Operators of Principal Type (1978) (55)
The Frobenius-Nirenberg theorem (1964) (55)
On the Uniqueness of the Cauchy Problem. (1958) (52)
Pseudo-differential operaors of type 1,1. (1988) (51)
A Remark on Perturbations of Compact Operators. (1994) (49)
A new proof and a generalization of an inequality of Bohr (1954) (49)
THE ASYMPTOTIC DISTRIBUTION OF EIGENVALUES OF PARTIAL DIFFERENTIAL OPERATORS (Translations of Mathematical Monographs 155) (1998) (48)
On the Uniqueness of the Cauchy Problem II. (1959) (46)
Lower bounds at infinity for solutions of differential equations with constant coefficients (1973) (44)
Hypoelliptic differential operators (1961) (43)
On the L2 continuity of pseudo‐differential operators (1971) (41)
Differential equations without solutions (1960) (41)
A Note on the Life-span of Classical Solutions to Nonlinear Wave Equations in Four Space Dimensions (2000) (36)
Non-uniqueness for the Cauchy Problem (1975) (36)
On the Fully Non-Linear Cauchy Problem with Small Data. II. (1991) (35)
Differentiability properties of solutions of systems of differential equations (1958) (35)
The null space of the $$-Neumann operator (2004) (35)
Some inequalities for functions of exponential type (1955) (34)
Hypoelliptic Convolution Equations. (1961) (32)
Remarks on the Klein-Gordon equation (1987) (32)
L2 estimates for Fourier integral operators with complex phase (1983) (30)
Free systems of vector fields (1978) (30)
Seminar on singularities of solutions of linear partial differential equations (1979) (29)
Supports and singular supports of convolutions (1963) (28)
On the Characteristic Cauchy Problem (1968) (22)
The Nash-Moser Theorem and Paradifferential Operators (1990) (21)
Remarks on Holmgren's uniqueness theorem (1993) (19)
Convolution equations in convex domains (1968) (19)
Hyperbolic systems with double characteristics (1993) (19)
Definitions of maximal differential operators (1958) (18)
Pseudo-Differential Operators of Principal Type (2009) (18)
Non-linear hyperbolic differential equations : lectures 1986-1987 (1988) (18)
Local and global properties of fundamental solutions (1957) (17)
A remark on Holmgren's uniqueness theorem (1971) (17)
NO PLANAR BILLIARD POSSESSES AN OPEN SET OF QUADRILATERAL TRAJECTORIES (2012) (16)
The fully non-linear Cauchy problem with small data (1989) (16)
Weak and strong extensions of differential operators (1961) (16)
Lectures on functions of several complex variables (1964) (15)
THE CALCULUS OF FOURIER INTEGRAL OPERATORS (1972) (15)
Strongly Subharmonic Functions. (1964) (15)
Seminar Notes on Pseudo-Differential Operators and Boundary Problems (1966) (14)
Why is there no nobel prize in Mathematics? (1985) (13)
A history of existence theorems for the Cauchy-Riemann complex inL2 spaces (2003) (13)
On the Legendre and Laplace transformations (1997) (12)
Limit sets of plurisubharmonic functions. (1989) (11)
On the subelliptic test estimates (1980) (11)
Null solutions of partial differential equations (1959) (10)
Growth properties of plurisubharmonic functions related to Fourier-Laplace transforms (1998) (10)
Second Order Elliptic Operators (2007) (10)
Partial differential equations and mathematical physics (1996) (8)
On the singularities of solutions of partial differential equations with constant coefficients (1972) (8)
Asgeirsson's Mean Value Theorem and Related Identities (2001) (8)
An Extension of Bohr's Inequality (1992) (8)
Between distributions and hyperfunctions (2019) (7)
The multinomial distribution and some Bergman kernels (2005) (6)
A counterexample of Gevrey class to the uniqueness of the Cauchy problem (2000) (6)
Differential operators with nonsingular characteristics (1962) (5)
The null space of the $\bar\partial $-Neumann operator@@@Le noyau de l'opérateur $\bar\partial$-Neumann (2004) (5)
Spectral Analysis of Singularities (1998) (4)
Microlocal analysis and applications : lectures given at the 2nd session of the Centro internazionale matematico estivo (C.I.M.E.) held at Montecatini Terme, Italy, July 3-11, 1989 (1991) (4)
The Fourier Transformation (2003) (4)
WEAK LINEAR CONVEXITY AND A RELATED NOTION OF CONCAVITY (2008) (4)
Unpublished Manuscripts: from 1951 to 2007 (2018) (4)
Preface to second edition (1973) (3)
The null space of the partial derivative-Neumann operator (2004) (3)
Fourier Integral Operators: Lectures at the Nordic Summer School of Mathematics (1969) (3)
Linear Partial Differential Operators /by Lars Hörmander (1964) (3)
Mathematics past and present : Fourier integral operators : selected classical articles (1994) (3)
The wave front set of the fundamental solution of a hyperbolic operator with double characteristics (1992) (3)
Inequalities Between Normal And Tangential Derivatives Of Harmonic Functions (2018) (3)
Advanced differential calculus (1994) (2)
The Cauchy problem for differential equations with constant coefficients (1969) (2)
The First Woman Professor and Her Male Colleague (1991) (2)
A remark on singular supports of convolutions. (1979) (2)
LOOKING FORWARD FROM ICM 1962 (1997) (1)
Remark to a Division Algorithm in the Proof of Oka ’ s First Coherence Theorem (2014) (1)
The Proof Of The Nirenberg-Treves Conjecture According To N. Dencker And N. Lerner (2018) (1)
Definition and Basic Properties of Distributions (1998) (1)
Partial Differential Equations and Mathematical Physics : The Danish-Swedish Analysis Seminar, 1995 (1996) (1)
The Diffusion Approximation In Neutron Transport Theory (2018) (1)
Differential Operators of Constant Strength (1963) (1)
Gårding’s Inequality During Three Decades (2018) (1)
A Paley–Wiener theorem for the analytic wave front set (1999) (1)
Distributions in Product Spaces (1998) (1)
On local integrability of fundamental solutions (1999) (1)
Correction To My Paper On Sobolev Spaces Associated With Some Lie Algebras (2018) (0)
Differential equations which have no solutions (1964) (0)
Approximation Of Solutions Of Constant Coefficient Boundary Problems And Of Entire Functions (2018) (0)
AUTOBIOGRAPHY OF LARS HÖRMANDER (1997) (0)
Some Tauberian Theorems Of Lewitan (2018) (0)
Composition with Smooth Maps (1998) (0)
The Mixed Dirichlet-Cauchy Problem for Second Order Operators (2007) (0)
Boundary Problems for Elliptic Differential Operators (2007) (0)
Some Classes of (Micro-)Hypoelliptic Operators (2007) (0)
An Isoperimetric Inequality In Homogeneous Finsler Spaces (2018) (0)
Elliptic boundary problems (1964) (0)
Lagrangian Distributions and Fourier Integral Operators (2009) (0)
Commentary on [16 ], [23] and [41] (1985) (0)
Approximation On Totally Real Manifolds (2018) (0)
Electromagnetic wave propagation over ground with small inhomogeneities in the electrical constants (2018) (0)
Interior regularity of solutions of differential equations (1964) (0)
Asymptotic behavior of Fourier-Laplace transform (1993) (0)
Fourier Multipliers With Small Norm (2018) (0)
The work of Carleson and Hoffman on bounded analytic functions in the disc (2018) (0)
The Cauchy problem (variable coefficients) (1964) (0)
General Mehler Formulas And The Weyl Calculus (2018) (0)
Guide To The Mathematical Models At The Department Of Mathematics In Lund (2018) (0)
Classes Of Infinitely Differentiable Functions (2018) (0)
Differentiation and Multiplication by Functions (1998) (0)
Lower Bounds For Subelliptic Operators (2018) (0)
Existence and approximation of solutions of differential equations (1964) (0)
The Cosine Theorem On A Surface And The Notion Of Curvature (2018) (0)
Symplectic Geometry And Differential Equations (2018) (0)
Proof Of The Existence Of Fundamental Solutions And Of Some Inequalities (2018) (0)
Analytic Function Theory and Differential Equations (2005) (0)
Some problems concerning linear partial differential equations (2018) (0)
The Cauchy problem (constant coefficients) (1964) (0)
Applications Of Helly’s Theorem To Estimates Of Tchebycheff Type (2018) (0)
Petrowsky’s L 2 Estimates For Hyperbolic Systems (2018) (0)
The Strictly Hyperbolic Cauchy Problem (2007) (0)
Elliptic Operators on a Compact Manifold Without Boundary (2007) (0)
The Dirichlet Problem In A Maximal Open Set (2018) (0)
On Best Approximation In L (2018) (0)
Remarks On Convexity With Respect To Operators Of Real Principal Type (2018) (0)
The Cauchy and Mixed Problems (2005) (0)
Long Range Scattering Theory (2009) (0)
Differential operators with simple characteristics (1963) (0)
Some special spaces of distributions (1963) (0)
Uniqueness for the Cauchy Problem (2009) (0)
Commentary on [39] and [47] (1985) (0)
Pseudo-Differential Operators and Boundary Problems (2018) (0)

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