Pluriharmonic function; function
Let
- <math>f \colon G \subset {\mathbb{C}}^n \to {\mathbb{C}}</math>
be a <math>C^2</math> (twice continuously differentiable) function. <math>f</math> is called pluriharmonic if for every complex line
- <math>\{ a + b z \mid z \in {\mathbb{C}} \}</math>
the function
- <math>z \mapsto f(a + bz)</math>
is a harmonic function on the set
- <math>\{ z \in {\mathbb{C}} \mid a + b z \in G \}</math>.
Notes
Every pluriharmonic function is a harmonic function, but not the other way around. Further, it can be shown that for holomorphic functions of several complex variables the real (and the imaginary) parts are locally pluriharmonic functions. However a function being harmonic in each variable separately does not imply that it is pluriharmonic.
Bibliography
- Steven G. Krantz. Function Theory of Several Complex Variables, AMS Chelsea Publishing, Providence, Rhode Island, 1992.
- Lower Your Summer Utility Bills « TEXAS HOME CENTRAL’s Blog Lower Your Summer Utility Bills. April 19th, 2007 — TexasHomeCentral If your neighbors also use a sprinkler system, reduce the watering time on the
- Cut Winter Utility Bills and Reduce the Carbon Footprint File Format: PDF/Adobe Acrobat - View as HTMLCut Winter Utility Bills and Reduce the Carbon Footprint. A Few Simple DIY Projects Can Save Homeowners Hundreds of Dollars. Huntersville, NC (September 14,
- Houston Window Company | Energy Saving Windows insulating windows in the gulf coast area. Cut your home utility bills in half by reducing the transfer of heat between the outside and inside of your home.
- GE Energy Star Dishwashers: Find, Compare, Read Reviews & Buy Built In Dishwashers - GE - Energy Star - Silver - Built In Dishwashers Dishwasher -Meets 2007 Energy Star Criteria - Can reduce utility bill b.
- Reduce Utility Bills - Water Heater Tips - HelpYourMoney.com The four main ways to reduce your water heating utility bills are as follows: Do you have more hot water heater tips to help reduce utility bills?
- Easy2Switch - reduce utility bills, save on domestic energy, cheap Easy2Switch can reduce your utility bills, helping you to save money on domestic energy and providing cheap business electricity and gas prices.
- Cut Utility Bills by Blocking Summer Heat Not only can trees reduce the monthly bills, they also add value to a property. An energy auditor from a local utility company can help decide which
- The efforts of your commanders and airmen to reduce utility File Format: Microsoft Word - View as HTMLEncourage Airmen to reduce utility bills and conserve resources using simple no-cost/low-cost strategies and a significant change in culture.
- How can I Reduce my Utility Bills? Brief and Straightforward Guide: How can I Reduce my Utility Bills?
- Earth Day Tips To Save Energy, Lower Utility Bills Routine maintenance and minor changes in how you use your appliances can reduce utility bills and contribute to a cleaner environment.
- Liberal Democrats : Greener swimming pools can reduce soaring Greener swimming pools can reduce soaring utility bills - Foster. 17 March 2006. Commenting on figures released today by the Local Government Association
- REDUCE UTILITY BILLS Reduce utility bills * money saving advice to reduce utility bills * reduce gas * electricity * broadband, internet, mobile phone & telephone bills * big