Analysis Meets Geometry The Mikael Passare Memorial Volume 1st Edition by Mats Andersson, Jan Boman, Christer Kiselman, Pavel Kurasov, Ragnar Sigurdsson ISBN 3319524690 9783319524696

Analysis Meets Geometry The Mikael Passare Memorial Volume 1st Edition by Mats Andersson, Jan Boman, Christer Kiselman, Pavel Kurasov, Ragnar Sigurdsson – Ebook PDF Instant Download/Delivery: 3319524690, 9783319524696
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ISBN 10: 3319524690 
ISBN 13: 9783319524696 
Author: Mats Andersson, Jan Boman, Christer Kiselman, Pavel Kurasov, Ragnar Sigurdsson

Analysis Meets Geometry The Mikael Passare Memorial Volume 1st Table of contents:

Part I Memorial Contributions
Mikael Passare
Curriculum Vitae
Mikael Passare’s Publications
List of Visited Countries
My Life with Mikael
World
Languages
Challenges
Home
Music
Projects
Personality
Thanks
Mikael Passare (1959–2011)
Mikael’s nine PhD students
Mikael’s mathematics
Residue theory
Residues in one complex variable.
Residues in several variables.
Lineal convexity
Amoebas and tropical geometry
The Pluricomplex Seminar
Lectures held by Mikael Passare.
The Nordan Meetings
Africa
Sonja Kovalevsky
Languages
An extraordinary curiosity
Music
A “Swedish Classic”
A passionate traveler
Finally
Two proposals
References
Sources
Mikael Passare
Part II Research Articles
Amoebas and Coamoebas of Linear Spaces
1. Introduction
2. Preliminaries
3. (Co)amoebas of complex algebraic varieties
4. (Co)Amoebas of linear spaces
4.1. (Co)Amoebas of lines in (C*) 1+m
5. Volume of (co)amoebas of k-dimensional very affine linear spaces in (C*)2k
References
One Parameter Regularizations of Products of Residue Currents
1. Introduction
2. Proof of Theorems 1.2 and 1.3
References
On the Effective Membership Problem for Polynomial Ideals
1. Introduction
2. Residue currents
2.1. Currents on a singular variety
2.2. Pseudomeromorphic currents
2.3. Residue currents associated with Hermitian complexes
2.4. BEF-varieties on singular varieties
2.5. The structure form ω on a singular variety
3. Gap sheaves and primary decomposition of sheaves
4. Resolutions of homogeneous ideals
5. Division problems on singular varieties
5.1. Distinguished varieties
6. Proofs
References
On the Optimal Regularity of Weak Geodesics in the Space of Metrics on a Polarized Manifold
1. Introduction
2. C1,1-regularity of solutions to complex Monge–Ampère equations over products
2.1. Notation: quasi-psh functions vs metrics on line bundles
2.2. The C1,1-regularity of weak geodesics
2.3. Further remarks
Acknowledgment
References
A Comparison Principle for Bergman Kernels
1. Introduction
2. The abstract setting
3. The proof of Theorem 1.1
References
Suita Conjecture from the One-dimensional Viewpoint
Introduction
1. Proof of the Suita conjecture
2. A Formula for the Bergman kernel
References
Siciak’s Theorem on Separate Analyticity
1. Introduction
2. Separate analyticity with boundedness assumption
3. The general case
References
Mikael Passare, a Jaunt in Approximation Theory
2. Back to Hermite
3. From Hermite to Kergin
4. Complex Kergin interpolation
5. Kergin and Fantappiè
6. Mean value interpolation
References
Amoebas and their Tropicalizations – a Survey
1. Introduction
2. Preliminaries
2.1. Amoebas
2.2. The tropical semi-ring
3. Valuations and the non-Archimedean amoeba
4. Maslov dequantization
5. The Archimedean tropical hypersurface and the complement induced tropical hypersurface
6. The spine
7. Summary and open problems
The non-Archimedean amoeba
The Archimedean tropical hypersurface
The complement induced tropical hypersurface
The spine
Acknowledgement
References
Coamoebas of Polynomials Supported on Circuits
1. Introduction
2. Coamoebas and lopsidedness
3. Real points and the coameoba of the A-discriminant
4. The space of coamoebas
4.1. Proof of Theorem 4.1
4.2. Proof of Theorem 4.2
5. The maximal area of planar circuit coamoebas
6. Critical points
7. On systems supported on a circuit
7.1. Reducing f(z) to a system of trinomials
7.2. Colopsidedness
7.3. Proof of Theorem 7.1
References
Limit of Green Functions and Ideals, the Case of Four Poles
1. Introduction
2. Statement of the results
2.1. Notations
2.2. The generic 4-pole case
2.3. Some singular cases
2.4. Upper and lower limits of ideals
3. Proof of Theorem 2.5
4. Proofs of Theorems 2.1, 2.2 and 2.3
4.1. Previous results
4.2. Proof of Theorem 2.1
4.3. Proof of Theorem 2.2
4.4. Proof of Theorem 2.3
References
Geodesics on Ellipsoids
1. Introduction
2. Axially symmetric surfaces and Hamiltonian formulation
3. Jacobi’s solution
4. Weierstrass’ solution and conserved quantities
5. Hamiltonian formulation with constraints
6. Level set Liouville integrability
References
Welschinger Invariants Revisited
Introduction
1. Definitions and main statements
1.1. Surfaces under consideration
1.2. Main results
2. Families of rational curves on rational surfaces
2.1. General setting
2.2. Curves on del Pezzo and uninodal del Pezzo surfaces
2.3. Deformation of isolated curve singularities
3. Proof of Theorem 6
3.1. Preliminary observations
3.2. Proof of Proposition 4
3.2.1. Moving a real point of configuration.
3.2.2. Moving a pair of imaginary conjugate points.
3.3. Proof of Proposition 5 and Theorem 6
Acknowledgement
References
Some Results on Amoebas and Coamoebas of Affine Spaces
1. Introduction
2. Preliminaries
3. Hyperplanes
4. Lines
5. Affine spaces of codimension n/2
6. A general approach for the study of the affine coamoeba
6.1. An indexation of the initial coamoebas
6.2. The compactified amoeba and the proof of Theorem 1.4
6.3. The contour of the coamoeba and partial proof of Theorem 1.3
6.4. Proof of Theorem 1.1 and the remaining proof of Theorem 1.3
6.5. An alternative notion of degeneracy
References
Convexity of Marginal Functions in the Discrete Case
Prologue
1. Introduction
1.1. The marginal function of a function of real variables
1.2. The marginal function of a function of integer variables
1.3. Relations between Minkowski addition, infimal convolution, and the operation of taking the marg
2. Other notions of discrete convexity
3. The convex hull and the convex envelope
4. The integer neighborhood and the canonical extension
5. Convolution and convex extensibility
6. Lateral convexity: Definition
7. Lateral convexity: Morphological aspects
8. Lateral convexity: Examples
9. Two variables: rhomboidal convexity
10. The set where the infimum is attained
11. Lateral convexity of marginal functions
11.1. Arbitrary dimensions
11.2. The case of two variables
11.3. Symmetric and asymmetric conditions
12. Necessity of lateral convexity
13. Conclusion
14. Hints for future work
14.1. Discrete convexity of infimal convolutions
14.2. Discrete convexity of p-marginal functions
14.3. Functions with integer values
14.4. Duality defined by convolution inequalities
References
Modules of Square Integrable Holomorphic Germs
1. Introduction
2. The proof of Theorem 1.1
3. Smooth Hermitian metrics and their curvature
4. Possibly singular Hermitian metrics
5. The δ-equation and Hörmander–Skoda type estimates
6. An extension theorem of Ohsawa–Takegoshi type
7. The proof of Theorem 1.2
References
An Effective Uniform Artin–Rees Lemma
1. Introduction
2. Andersson–Wulcan currents and the diamond product
3. The proof of Theorem 1.1
4. The proof of Theorem 1.6
5. The non-smooth case
Acknowledgment
References
Amoebas of Half-dimensional Varieties
1. Introduction
1.1. Definitions
1.2. Statement of the results
2. Proof of the theorem
2.1. Bounds for the number of inverse images for the amoeba and coamoeba maps
2.2. Estimating the volume of amoeba
3. Some remarks and open problems
3.1. Example: linear spaces in CP2n
3.2. MultiHarnack varieties in RP2n
3.3. Foliation of A
3.4. Dimensions greater than a half
References
A log Canonical Threshold Test
1. Introduction and statement of results
2. Proofs
References
Root-counting Measures of Jacobi Polynomials and Topological Types and Critical Geodesics of Related
1. Introduction: From Jacobi polynomials to quadratic differentials
2. Proof of Theorem 1
3. Preliminaries on quadratic differentials
4. Cauchy transforms satisfying quadratic equations and quadratic differentials
5. Does weak convergence of Jacobi polynomials imply stronger forms of convergence?
6. Domain configurations of normalized quadratic differentials
7. How parameters determine the type of domain configuration
8. Identifying simple critical geodesics and critical loops
9. How parameters count critical geodesics and critical loops
10. Some related questions
11. Figures Zoo
Acknowledgement.
References
Interior Eigenvalue Density of Jordan Matrices with Random Perturbations
1. Introduction
Perturbations of Jordan blocks
2. Numerical simulations
3. A general formula
4. Grushin problem for the perturbed Jordan block
4.1. Setting up an auxiliary problem
4.2. Estimates for the effective Hamiltonian
5. Choosing appropriate coordinates
6. Proof of Theorem 1.2

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Tags: Mats Andersson, Jan Boman, Christer Kiselman, Pavel Kurasov, Ragnar Sigurdsson, Analysis Meets, Mikael Passare