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I have created a "GeoStatistical Analyst Layer" with "Diffusion Interpolation with Barriers" tool and then I published it on the ArcGIS for Server.

How can I show this layer in my web map application using Javascript API?

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In the list of layer types that dynamic map service supports, there is also support for Geostatistical layer. Which means you can access your dynamic map service that contains a Geostatistical layer without any extra processing.

Since you are on Esri JS API for ArcGIS, you would need to look for the sample that just draws a dynamic map service such as this. You basically need to declare a variable

var dynamicMapServiceLayer = new ArcGISDynamicMapServiceLayer("http://sampleserver1.arcgisonline.com/ArcGIS/rest/services/Demographics/ESRI_Population_World/MapServer"

and point it to the MapServer REST endpoint of your service published which follows the notation http://%machinename%:6080/ArcGIS/rest/services/servicename/MapServer. You can find out what services you have and the URLs they have via a special application installed with ArcGIS for Server called Services Directory. You can access this application at http://%machinename%:6080/ArcGIS/rest/services.

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